Home >> The gfun package

# The gfun package

Gfun is a Maple package that provides tools for

• guessing a sequence or a series from its first terms;
• manipulating rigorously solutions of linear differential or recurrence equations, using the equation as a data-structure.

gfun 3.76 (July 2015):

Once downloaded, see the help page of libname to understand how to make them available from Maple. Typically, your session will contain something like libname:="gfun_path",libname:

You can check that this worked by asking gfun:-version(); that should return the number above.

The source code can be read by anyone who can read Maple code, but if you want to use the package, then it’s better to download it with the link above.

## Help pages

All the help pages are available directly from within Maple, and here are pdf versions:

## Reference for gfun

The primary reference to use when citing gfun is the following one:

• Bruno Salvy and Paul Zimmermann. — Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable. — 20.2:163-177, 1994.
doi:10.1145/178365.178368
[BibTeX] [Abstract] [PDF from ACM]
We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended both as an elementary introduction to the subject and as a reference manual for the package.

@article{SalvyZimmermann1994,
Author = {Salvy, Bruno and Zimmermann, Paul},
Date-Modified = {2016-05-11 05:46:50 +0000},
Doi = {10.1145/178365.178368},
Journal = toms,
Number = {2},
Owner = {bs},
Pages = {163--177},
Title = {Gfun: a {M}aple package for the manipulation of generating and holonomic functions in one variable},
Url = {http://dl.acm.org/authorize?N02903},
Volume = {20},
Year = {1994},
Abstract = {We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended both as an elementary introduction to the subject and as a reference manual for the package.
}}

If you are using the NumGfun subpackage, then the proper reference is:

• Marc Mezzarobba. — Numgfun: a package for numerical and analytic computation with D-finite functions. — Proceedings of the 2010 international symposium on symbolic and algebraic computation (issac 2010), ACM, pages 139-145, 2010.
arXiv:abs/1002.3077
doi:10.1145/1837934.1837965
[BibTeX] [Abstract]
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky. In some cases, our descriptions contain small improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.

@inproceedings{Mezzarobba2010,
Arxiv = {abs/1002.3077},
Author = {Mezzarobba, Marc},
Booktitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010)},
Date-Modified = {2013-03-05 09:54:09 +0000},
Doi = {10.1145/1837934.1837965},
Pages = {139--145},
Publisher = {ACM},
Title = {NumGfun: a Package for Numerical and Analytic Computation with {D}-finite Functions},
Year = {2010},
Abstract = {This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky. In some cases, our descriptions contain small improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.},
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## Articles citing gfun

The following is a list of articles that cite gfun. If you know of an article that is not in this list, but does cite gfun, please send me an email so that I can add it to this list.

### 2016

• A. Bostan, G. Chèze, T. Cluzeau, and J. -A. Weil. — Efficient algorithms for computing rational first integrals and darboux polynomials of planar polynomial vector fields. — Mathematics of computation, 85.299:1393-1425, 2016.
[BibTeX]
@article{BostanChezeCluzeauWeil2016,
Author = {Bostan, A. and Ch{\e}ze, G. and Cluzeau, T. and Weil, J.-A.},
Date-Modified = {2016-03-15 09:41:55 +0000},
Document_Type = {Article},
Journal = {Mathematics of Computation},
Number = {299},
Pages = {1393-1425},
Title = {Efficient algorithms for computing rational first integrals and darboux polynomials of planar polynomial vector fields},
Volume = {85},
Year = {2016}
}

### 2015

• Michael Albert and Mireille Bousquet-Mélou. — Permutations sortable by two stacks in parallel and quarter plane walks. — European j. combin., 43 131-164, 2015.
[BibTeX]
@article{AlbertBousquet-Melou2015,
Author = {Albert, Michael and Bousquet-M{\'e}lou, Mireille},
Date-Modified = {2015-01-23 14:06:17 +0000},
Fjournal = {European Journal of Combinatorics},
Issn = {0195-6698},
Journal = {European J. Combin.},
Mrclass = {05A05 (68R15)},
Mrnumber = {3266288},
Pages = {131--164},
Title = {Permutations sortable by two stacks in parallel and quarter plane walks},
Volume = {43},
Year = {2015},
}

### 2014

• William Y. C. Chen, Qiang-Hui Guo, Lisa H. Sun, and Jian Wang. — Zigzag stacks and m-regular linear stacks. — Journal of computational biology, 21.12:915-935, 2015/01/23 2014.
[BibTeX]
@article{ChenGuoSunWang2014,
Author = {Chen, William Y. C. and Guo, Qiang-Hui and Sun, Lisa H. and Wang, Jian},
Booktitle = {Journal of Computational Biology},
Da = {2014/12/01},
Date = {2014/12/01},
Date-Modified = {2015-01-23 14:06:07 +0000},
Isbn = {1066-5277},
Journal = {Journal of Computational Biology},
M3 = {doi: 10.1089/cmb.2014.0133},
Month = {2015/01/23},
Number = {12},
Pages = {915--935},
Publisher = {Mary Ann Liebert, Inc., publishers},
Title = {Zigzag Stacks and m-Regular Linear Stacks},
Ty = {JOUR},
Volume = {21},
Year = {2014},
Year1 = {2014},
Annote = {doi: 10.1089/cmb.2014.0133},
Bdsk-Url-1 = {http://dx.doi.org/10.1089/cmb.2014.0133}}

• Manuel Kauers. — Bounds for d-finite closure properties. — Proceedings of the 39th international symposium on symbolic and algebraic computation, New York, NY, USA: ACM, pages 288-295, 2014.
[BibTeX]
@inproceedings{Kauers2014,
Acmid = {2608634},
Address = {New York, NY, USA},
Author = {Kauers, Manuel},
Booktitle = {Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation},
Date-Modified = {2015-01-23 14:05:57 +0000},
Isbn = {978-1-4503-2501-1},
Keywords = {holonomic functions, ore operators},
Location = {Kobe, Japan},
Numpages = {8},
Pages = {288--295},
Publisher = {ACM},
Series = {ISSAC '14},
Title = {Bounds for D-finite Closure Properties},
Year = {2014},
Bdsk-Url-1 = {http://doi.acm.org/10.1145/2608628.2608634},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/2608628.2608634}}

### 2013

• W. A. Lorenz and Y. Ponty. — Non-redundant random generation algorithms for weighted context-free grammars. — Theoretical computer science, 502 177-194, 2013.
[BibTeX]
@article{LorenzPonty2013,
Author = {Lorenz, W. A. and Ponty, Y.},
Date-Modified = {2013-09-26 05:38:33 +0000},
Journal = {Theoretical Computer Science},
Pages = {177-194},
Title = {Non-redundant random generation algorithms for weighted context-free grammars},
Volume = {502},
Year = {2013},
Bdsk-Url-1 = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84884285265&partnerID=40&md5=7680ad4295d33c8898bbb7bcc7be5594}}

• Kealey Dias. — Enumerating combinatorial classes of the complex polynomial vector fields in $\mathbb C$. — Ergodic theory and dynamical systems, 33.2:416-440, 2013.
[BibTeX]
@article{Dias2013,
Author = {Dias, Kealey},
Date-Modified = {2013-06-06 06:31:43 +0000},
Journal = {Ergodic Theory and Dynamical Systems},
Number = {2},
Pages = {416--440},
Title = {Enumerating combinatorial classes of the complex polynomial vector fields in $\mathbb C$},
Volume = {33},
Year = {2013}}

• Sven Beuchler, Veronika Pillwein, and Sabine Zaglmayr. — Sparsity optimized high order finite element functions for on tetrahedra. — Advances in applied mathematics, 50.5:749-769, 2013.
[BibTeX]
@article{BeuchlerPillweinZaglmayr2013,
Author = {Beuchler, Sven and Pillwein, Veronika and Zaglmayr, Sabine},
Date-Modified = {2015-01-23 13:41:19 +0000},
Issn = {0196-8858},
Journal = {Advances in Applied Mathematics},
Number = 5,
Pages = {749 -- 769},
Title = {Sparsity optimized high order finite element functions for on tetrahedra},
Volume = 50,
Year = 2013}

• T. Combot. — Integrability conditions at order 2 for homogeneous potentials of degree -1. — Nonlinearity, 26.1:95-120, 2013.
[BibTeX]
@article{Combot2013,
Author = {Combot, T.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Nonlinearity},
Number = {1},
Pages = {95-120},
Title = {Integrability conditions at order 2 for homogeneous potentials of degree -1},
Volume = {26},
Year = {2013}}

### 2012

• M. Elder, A. Rechnitzer, and T. Wong. — On the cogrowth of thompson’s group f. — Groups, complexity, cryptology, 4.2:301-320, 2012.
[BibTeX]
@article{ElderRechnitzerWong2012,
Author = {Elder, M. and Rechnitzer, A. and Wong, T.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Groups, Complexity, Cryptology},
Number = {2},
Pages = {301-320},
Title = {On the cogrowth of Thompson's group F},
Volume = {4},
Year = {2012}}

• B. Buchberger and M. Rosenkranz. — Transforming problems from analysis to algebra: a case study in linear boundary problems. — Journal of symbolic computation, 47.6:589-609, 2012.
[BibTeX]
@article{BuchbergerRosenkranz2012,
Author = {Buchberger, B. and Rosenkranz, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {6},
Pages = {589-609},
Title = {Transforming problems from analysis to algebra: A case study in linear boundary problems},
Volume = {47},
Year = {2012}}

• N. Brisebarre, M. Joldes, É. Martin-Dorel, M. Mayero, J. -M. Muller, I. Pasca, L. Rideau, and L. Théry. — Rigorous polynomial approximation using Taylor models in Coq. — pages 85-99, 2012.
[BibTeX]
@inproceedings{BrisebarreJoldesMartin-DorelMayeroMullerPascaRideauThery2012,
Author = {Brisebarre, N. and Joldes, M. and Martin-Dorel, {\'E}. and Mayero, M. and Muller, J.-M. and Pasca, I. and Rideau, L. and Th{\'e}ry, L.},
Date-Modified = {2013-03-05 09:59:07 +0000},
Pages = {85-99},
Series = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
Title = {Rigorous polynomial approximation using {T}aylor models in {C}oq},
Volume = {7226 LNCS},
Year = {2012}}

• M. Bousquet-Mélou, E. Fusy, and L. -. Préville-Ratelle. — The number of intervals in the m-tamari lattices. — Electronic journal of combinatorics, 18.2:1-26, 2012.
[BibTeX]
@article{Bousquet-MelouFusyPreville-Ratelle2012,
Author = {Bousquet-M{\'e}lou, M. and Fusy, E. and Pr{\'e}ville-Ratelle, L. -.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Journal of Combinatorics},
Number = {2},
Pages = {1-26},
Title = {The number of intervals in the m-Tamari lattices},
Volume = {18},
Year = {2012}}

### 2011

• A. Al-Salman, M. B. H. Rhouma, and A. A. Al-Jarrah. — On integrals and sums involving special functions. — Missouri journal of mathematical sciences, 23.2:123-141, 2011.
[BibTeX]
@article{Al-SalmanRhoumaAl-Jarrah2011,
Author = {Al-Salman, A. and Rhouma, M. B. H. and Al-Jarrah, A. A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Missouri Journal of Mathematical Sciences},
Number = {2},
Pages = {123-141},
Title = {On integrals and sums involving special functions},
Volume = {23},
Year = {2011}}

• G. Labelle and A. Lacasse. — Closed paths whose steps are roots of unity. — Fpsac’11 – 23rd international conference on formal power series and algebraic combinatorics, pages 599-610, 2011.
[BibTeX]
@inproceedings{LabelleLacasse2011,
Author = {Labelle, G. and Lacasse, A.},
Booktitle = {FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {599-610},
Title = {Closed paths whose steps are roots of unity},
Year = {2011}}

• O. Bernardi and M. Bousquet-Mélou. — Counting colored planar maps: algebraicity results. — Journal of combinatorial theory.series b, 101.5:315-377, 2011.
[BibTeX]
@article{BernardiBousquet-Melou2011,
Author = {Bernardi, O. and Bousquet-M{\'e}lou, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Combinatorial Theory.Series B},
Number = {5},
Pages = {315-377},
Title = {Counting colored planar maps: Algebraicity results},
Volume = {101},
Year = {2011}}

• W. Hebisch and M. Rubey. — Extended rate, more gfun. — Journal of symbolic computation, 46.8:889-903, 2011.
[BibTeX]
@article{HebischRubey2011,
Author = {Hebisch, W. and Rubey, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {8},
Pages = {889-903},
Title = {Extended rate, more GFUN},
Volume = {46},
Year = {2011}}

• M. Kauers. — The concrete tetrahedron. — Proceedings of the international symposium on symbolic and algebraic computation, issac, pages 7, 2011.
[BibTeX]
@inproceedings{Kauers2011,
Author = {Kauers, M.},
Booktitle = {Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {7},
Title = {The concrete tetrahedron},
Year = {2011}}

• A. Bostan, F. Chyzak, Z. Li, and B. Salvy. — Fast computation of common left multiples of linear ordinary differential operators. — Acm communications in computer algebra, 45.1-2:111-112, 2011.
[BibTeX]
@article{BostanChyzakLiSalvy2011,
Author = {Bostan, A. and Chyzak, F. and Li, Z. and Salvy, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {ACM Communications in Computer Algebra},
Number = {1-2},
Pages = {111-112},
Title = {Fast computation of common left multiples of linear ordinary differential operators},
Volume = {45},
Year = {2011}}

### 2010

• Marc Mezzarobba. — Numgfun: a package for numerical and analytic computation with D-finite functions. — Proceedings of the 2010 international symposium on symbolic and algebraic computation (issac 2010), ACM, pages 139-145, 2010.
arXiv:abs/1002.3077
doi:10.1145/1837934.1837965
[BibTeX] [Abstract]
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky. In some cases, our descriptions contain small improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.

@inproceedings{Mezzarobba2010,
Arxiv = {abs/1002.3077},
Author = {Mezzarobba, Marc},
Booktitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010)},
Date-Modified = {2013-03-05 09:54:09 +0000},
Doi = {10.1145/1837934.1837965},
Pages = {139--145},
Publisher = {ACM},
Title = {NumGfun: a Package for Numerical and Analytic Computation with {D}-finite Functions},
Year = {2010},
Abstract = {This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky. In some cases, our descriptions contain small improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.},
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• A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, and B. Salvy. — The dynamic dictionary of mathematical functions (ddmf). — pages 35-41, 2010.
[BibTeX]
@inproceedings{BenoitChyzakDarrasseGerholdMezzarobbaSalvy2010,
Author = {Benoit, A. and Chyzak, F. and Darrasse, A. and Gerhold, S. and Mezzarobba, M. and Salvy, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {35-41},
Series = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
Title = {The Dynamic Dictionary of Mathematical Functions (DDMF)},
Volume = {6327 LNCS},
Year = {2010}}

• A. Bostan, B. Salvy, and K. Tran. — Generating functions of chebyshev-like polynomials. — International journal of number theory, 6.7:1659-1667, 2010.
[BibTeX]
@article{BostanSalvyTran2010,
Author = {Bostan, A. and Salvy, B. and Tran, K.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {International Journal of Number Theory},
Number = {7},
Pages = {1659-1667},
Title = {Generating functions of Chebyshev-like polynomials},
Volume = {6},
Year = {2010}}

• M. Mezzarobba and B. Salvy. — Effective bounds for p-recursive sequences. — Journal of symbolic computation, 45.10:1075-1096, 2010.
[BibTeX]
@article{MezzarobbaSalvy2010,
Author = {Mezzarobba, M. and Salvy, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {10},
Pages = {1075-1096},
Title = {Effective bounds for P-recursive sequences},
Volume = {45},
Year = {2010}}

• A. Denise, Y. Ponty, and M. Termier. — Controlled non-uniform random generation of decomposable structures. — Theoretical computer science, 411.40-42:3527-3552, 2010.
[BibTeX]
@article{DenisePontyTermier2010,
Author = {Denise, A. and Ponty, Y. and Termier, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {40-42},
Pages = {3527-3552},
Title = {Controlled non-uniform random generation of decomposable structures},
Volume = {411},
Year = {2010}}

• A. Bostan, M. Kauers, and M. V. Hoeij. — The complete generating function for gessel walks is algebraic. — Proceedings of the american mathematical society, 138.9:3063-3078, 2010.
[BibTeX]
@article{BostanKauersHoeij2010,
Author = {Bostan, A. and Kauers, M. and Hoeij, M. V.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Proceedings of the American Mathematical Society},
Number = {9},
Pages = {3063-3078},
Title = {The complete generating function for gessel walks is algebraic},
Volume = {138},
Year = {2010}}

• R. Bacher and P. Flajolet. — Pseudo-factorials, elliptic functions, and continued fractions. — Ramanujan journal, 21.1:71-97, 2010.
[BibTeX]
@article{BacherFlajolet2010,
Author = {Bacher, R. and Flajolet, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Ramanujan Journal},
Number = {1},
Pages = {71-97},
Title = {Pseudo-factorials, elliptic functions, and continued fractions},
Volume = {21},
Year = {2010}}

### 2009

• W. Y. C. Chen, H. S. W. Han, and C. M. Reidys. — Random k-noncrossing rna structures. — Proceedings of the national academy of sciences of the united states of america, 106.52:22061-22066, 2009.
[BibTeX]
@article{ChenHanReidys2009,
Author = {Chen, W. Y. C. and Han, H. S. W. and Reidys, C. M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Proceedings of the National Academy of Sciences of the United States of America},
Number = {52},
Pages = {22061-22066},
Title = {Random k-noncrossing RNA structures},
Volume = {106},
Year = {2009}}

• P. L. Douillet. — Sampling distribution of the variance. — Proceedings – winter simulation conference, pages 403-414, 2009.
[BibTeX]
@inproceedings{Douillet2009,
Author = {Douillet, P. L.},
Booktitle = {Proceedings - Winter Simulation Conference},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {403-414},
Title = {Sampling distribution of the variance},
Year = {2009}}

• A. Bostan and M. Kauers. — Automatic classification of restricted lattice walks. — Fpsac’09 – 21st international conference on formal power series and algebraic combinatorics, pages 201-215, 2009.
[BibTeX]
@inproceedings{BostanKauers2009,
Author = {Bostan, A. and Kauers, M.},
Booktitle = {FPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {201-215},
Title = {Automatic classification of restricted lattice walks},
Year = {2009}}

• J. Blümlein, M. Kauers, S. Klein, and C. Schneider. — Determining the closed forms of the o (as 3) anomalous dimensions and wilson coefficients from mellin moments by means of computer algebra. — Computer physics communications, 180.11:2143-2165, 2009.
[BibTeX]
@article{BlumleinKauersKleinSchneider2009,
Author = {Bl{\"u}mlein, J. and Kauers, M. and Klein, S. and Schneider, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Computer Physics Communications},
Number = {11},
Pages = {2143-2165},
Title = {Determining the closed forms of the O (as 3) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra},
Volume = {180},
Year = {2009}}

• P. -. Koseleff and D. Pecker. — A polynomial parametrization of torus knots. — Applicable algebra in engineering, communications and computing, 20.5-6:361-377, 2009.
[BibTeX]
@article{KoseleffPecker2009,
Author = {Koseleff, P. -. and Pecker, D.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Applicable Algebra in Engineering, Communications and Computing},
Number = {5-6},
Pages = {361-377},
Title = {A polynomial parametrization of torus knots},
Volume = {20},
Year = {2009}}

• J. van der Hoeven. — On asymptotic extrapolation. — Journal of symbolic computation, 44.8:1000-1016, 2009.
[BibTeX]
@article{Hoeven2009,
Author = {van der Hoeven, J.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {8},
Pages = {1000-1016},
Title = {On asymptotic extrapolation},
Volume = {44},
Year = {2009}}

• M. Kauers and C. Koutschan. — A mathematica package for q-holonomic sequences and power series. — Ramanujan journal, 19.2:137-150, 2009.
[BibTeX]
@article{KauersKoutschan2009,
Author = {Kauers, M. and Koutschan, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Ramanujan Journal},
Number = {2},
Pages = {137-150},
Title = {A Mathematica package for q-holonomic sequences and power series},
Volume = {19},
Year = {2009}}

• A. Rechnitzer. — The anisotropic generating function of self-avoiding polygons is not d-finite. — pages 93-115, 2009.
[BibTeX]
@inproceedings{Rechnitzer2009,
Author = {Rechnitzer, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {93-115},
Series = {Lecture Notes in Physics},
Title = {The anisotropic generating function of self-avoiding polygons is not d-finite},
Volume = {775},
Year = {2009}}

• S. Gerhold and R. Warnung. — Finding efficient recursions for risk aggregation by computer algebra. — Journal of computational and applied mathematics, 223.1:499-507, 2009.
[BibTeX]
@article{GerholdWarnung2009,
Author = {Gerhold, S. and Warnung, R.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Computational and Applied Mathematics},
Number = {1},
Pages = {499-507},
Title = {Finding efficient recursions for risk aggregation by computer algebra},
Volume = {223},
Year = {2009}}

### 2008

• Jun Zhang. — Sumudu transform based coefficients calculation. — Nonlinear studies, 15.4:355-372, 2008.
[BibTeX]
@article{Zhang2008,
Author = {Zhang, Jun},
Date-Modified = {2013-03-05 09:17:44 +0000},
Issn = {1359-8678},
Journal = {Nonlinear Studies},
Mrclass = {44A15 (68W30)},
Mrnumber = {MR2483147},
Number = {4},
Pages = {355--372},
Title = {Sumudu transform based coefficients calculation},
Volume = {15},
Year = {2008}}

• Helmut Prodinger. — On the order of the recursion relation of Motzkin numbers of higher rank. — Open appl. math. j., 2 14-15, 2008.
doi:10.2174/1874114200802010014
[BibTeX] [PDF]
@article{Prodinger2008a,
Author = {Prodinger, Helmut},
Date-Modified = {2013-03-05 09:17:19 +0000},
Doi = {10.2174/1874114200802010014},
Fjournal = {Open Applied Mathematics Journal},
Issn = {1874-1142},
Journal = {Open Appl. Math. J.},
Mrclass = {05A15},
Mrnumber = {2399687 (2009d:05013)},
Mrreviewer = {Asamoah Nkwanta},
Pages = {14--15},
Title = {On the order of the recursion relation of {M}otzkin numbers of higher rank},
Url = {http://dx.doi.org/10.2174/1874114200802010014},
Volume = {2},
Year = {2008},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2399687}}

• Georgy P. Egorychev and Eugene V. Zima. — Integral representation and algorithms for closed form summation. — Ed. M. Hazewinkel. Vol. 5. Handbook of Algebra. North-Holland, 2008. 459-529.
doi:DOI: 10.1016/S1570-7954(07)05009-7
[BibTeX] [Abstract] [PDF]
The problem of computation and estimation of finite and infinite sums (generating functions) often arises in combinatorics and graph theory, theory of algorithms and computer algebra, group theory and function theory, probability theory and asymptotical analysis as well as in physics, statistical mechanics, and other areas of knowledge. This article is intended for a wide audience including graduate students and researchers in the various applied fields. Here we present the history, main results, model examples, various applications and perspectives of investigation in two connected general approaches to summation: the integral representation and computation of combinatorial sums (“the method of coefficients”) and the modern algorithmic approach. Each of the approaches is based on classic results of mathematical analysis, function theory and computer algebra.

@incollection{EgorychevZima2008a,
Author = {Egorychev, Georgy P. and Zima, Eugene V.},
Date-Modified = {2013-03-05 09:16:05 +0000},
Doi = {DOI: 10.1016/S1570-7954(07)05009-7},
Editor = {Hazewinkel, M.},
Issn = {1570-7954},
Pages = {459 - 529},
Publisher = {North-Holland},
Series = {Handbook of Algebra},
Title = {Integral Representation and Algorithms for Closed Form Summation},
Url = {http://www.sciencedirect.com/science/article/B8JBW-4RY6KBH-J/2/f7562fd3c2235b536840da80324e90bf},
Volume = {5},
Year = {2008},
Abstract = {
The problem of computation and estimation of finite and infinite sums (generating functions) often arises in combinatorics and graph theory, theory of algorithms and computer algebra, group theory and function theory, probability theory and asymptotical analysis as well as in physics, statistical mechanics, and other areas of knowledge.
This article is intended for a wide audience including graduate students and researchers in the various applied fields. Here we present the history, main results, model examples, various applications and perspectives of investigation in two connected general approaches to summation: the integral representation and computation of combinatorial sums (the method of coefficients'') and the modern algorithmic approach. Each of the approaches is based on classic results of mathematical analysis, function theory and computer algebra.},
Bdsk-Url-1 = {http://dx.doi.org/10.1016/S1570-7954(07)05009-7}}

• Jonathan M. Borwein and Bruno Salvy. — A proof of a recursion for Bessel moments. — Experimental mathematics, 17.2:223-230, 2008.
arXiv:abs/0706.1409
[BibTeX] [Abstract] [PDF]
We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $K_0$.

@article{BorweinSalvy2008,
Arxiv = {abs/0706.1409},
Author = {Borwein, Jonathan M. and Salvy, Bruno},
Date-Modified = {2013-03-05 09:15:23 +0000},
Journal = {Experimental Mathematics},
Number = {2},
Pages = {223--230},
Title = {A proof of a recursion for {B}essel moments},
Url = {http://projecteuclid.org/euclid.em/1227118973},
Volume = {17},
Year = {2008},
Abstract = {We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $K_0$.
},
Bdsk-Url-1 = {http://projecteuclid.org/euclid.em/1227118973}}

• Arvind Ayyer and Doron Zeilberger. — Two dimensional directed lattice walks with boundaries. — Tapas in experimental mathematics. Vol. 457. Contemp. Math.. Providence, RI: Amer. Math. Soc., 2008. 1-19.
doi:10.1090/conm/457/08900
[BibTeX] [PDF]
@incollection{AyyerZeilberger2008,
Author = {Ayyer, Arvind and Zeilberger, Doron},
Booktitle = {Tapas in experimental mathematics},
Date-Modified = {2013-03-05 09:14:35 +0000},
Doi = {10.1090/conm/457/08900},
Mrclass = {05A15 (82B20 82B41 82D60)},
Mrnumber = {2427662 (2009i:05009)},
Mrreviewer = {B. L. Granovsky},
Pages = {1--19},
Publisher = {Amer. Math. Soc.},
Series = {Contemp. Math.},
Title = {Two dimensional directed lattice walks with boundaries},
Url = {http://dx.doi.org/10.1090/conm/457/08900},
Volume = {457},
Year = {2008},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2427662}}

• S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, and B. Zimmermann. — Computing the complexity for schelling segregation models. — Communications in nonlinear science and numerical simulation, 13.10:2236-2245, 2008.
[BibTeX]
@article{GerholdGlebskySchneiderWeissZimmermann2008,
Author = {Gerhold, S. and Glebsky, L. and Schneider, C. and Weiss, H. and Zimmermann, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Communications in Nonlinear Science and Numerical Simulation},
Number = {10},
Pages = {2236-2245},
Title = {Computing the complexity for Schelling segregation models},
Volume = {13},
Year = {2008}}

• N. R. Rao and A. Edelman. — The polynomial method for random matrices. — Foundations of computational mathematics, 8.6:649-702, 2008.
[BibTeX]
@article{RaoEdelman2008,
Author = {Rao, N. R. and Edelman, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Foundations of Computational Mathematics},
Number = {6},
Pages = {649-702},
Title = {The polynomial method for random matrices},
Volume = {8},
Year = {2008}}

• M. Kauers and B. Zimmermann. — Computing the algebraic relations of c-finite sequences and multisequences. — Journal of symbolic computation, 43.11:787-803, 2008.
[BibTeX]
@article{KauersZimmermann2008,
Author = {Kauers, M. and Zimmermann, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {11},
Pages = {787-803},
Title = {Computing the algebraic relations of C-finite sequences and multisequences},
Volume = {43},
Year = {2008}}

• J. Carette, S. Smith, J. McCutchan, C. Anand, and A. Korobkine. — Case studies in model manipulation for scientific computing. — pages 24-37, 2008.
[BibTeX]
@inproceedings{CaretteSmithMcCutchanAnandKorobkine2008,
Author = {Carette, J. and Smith, S. and McCutchan, J. and Anand, C. and Korobkine, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {24-37},
Series = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
Title = {Case studies in model manipulation for scientific computing},
Volume = {5144 LNAI},
Year = {2008}}

• O. Bernardi. — On triangulations with high vertex degree. — Annals of combinatorics, 12.1:17-44, 2008.
[BibTeX]
@article{Bernardi2008,
Author = {Bernardi, O.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Annals of Combinatorics},
Number = {1},
Pages = {17-44},
Title = {On triangulations with high vertex degree},
Volume = {12},
Year = {2008}}

• Y. Ponty. — Efficient sampling of rna secondary structures from the boltzmann ensemble of low-energy : ttthe boustrophedon method. — Journal of mathematical biology, 56.1-2:107-127, 2008.
[BibTeX]
@article{Ponty2008,
Author = {Ponty, Y.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of mathematical biology},
Number = {1-2},
Pages = {107-127},
Title = {Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy : Ttthe boustrophedon method},
Volume = {56},
Year = {2008}}

• W. A. Lorenz, Y. Ponty, and P. Clote. — Asymptotics of rna shapes. — Journal of computational biology, 15.1:31-63, 2008.
[BibTeX]
@article{LorenzPontyClote2008,
Author = {Lorenz, W. A. and Ponty, Y. and Clote, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Computational Biology},
Number = {1},
Pages = {31-63},
Title = {Asymptotics of RNA shapes},
Volume = {15},
Year = {2008}}

### 2007

• Carsten Schneider. — Symbolic summation assists combinatorics. — Séminaire lotharingien de combinatoire, 56.B56b:1-36, 2007.
[BibTeX]
@article{Schneider2007a,
Author = {Schneider, Carsten},
Date-Modified = {2013-03-05 09:20:34 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Number = {B56b},
Pages = {1--36},
Title = {Symbolic summation assists combinatorics},
Volume = {56},
Year = {2007},
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• P. Paule and C. Schneider. — Truncating binomial series with symbolic summation. — Integers. electronic journal of combinatorial number theory, 7.A22:1-9, 2007.
[BibTeX] [PDF]
@article{PauleSchneider2007,
Author = {Paule, P. and Schneider, C.},
Date-Modified = {2013-03-05 09:20:00 +0000},
Isbn_Issn = {ISSN 1553-1732},
Journal = {INTEGERS. Electronic Journal of Combinatorial Number Theory},
Language = {english},
Length = {9},
Number = {A22},
Pages = {1--9},
Refereed = {yes},
Title = {Truncating Binomial Series with Symbolic Summation},
Url = {http://www.integers-ejcnt.org/vol7.html},
Volume = {7},
Year = {2007},
Bdsk-Url-1 = {http://www.integers-ejcnt.org/vol7.html}}

• Éric Fusy. — Counting unrooted maps using tree-decomposition. — Séminaire lotharingien de combinatoire, 54A 1-44, 2007.
[BibTeX]
@article{Fusy2007,
Author = {Fusy, {\'E}ric},
Date-Modified = {2013-03-05 09:18:58 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Pages = {1--44},
Title = {Counting Unrooted Maps Using Tree-Decomposition},
Volume = {54A},
Year = {2007},
Bdsk-File-1 = {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}}

• Manuel Bodirsky, Clemens Gröpl, Daniel Johannsen, and Mihyun Kang. — A direct decomposition of 3-connected planar graphs. — Séminaire lotharingien de combinatoire, 54a.B54Ak:1-15, 2007.
[BibTeX]
@article{BodirskyGroplJohannsenKang2007,
Author = {Bodirsky, Manuel and Gr{\"o}pl, Clemens and Johannsen, Daniel and Kang, Mihyun},
Date-Modified = {2013-03-05 09:18:23 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Number = {B54Ak},
Pages = {1--15},
Title = {A direct decomposition of 3-connected planar graphs},
Volume = {54a},
Year = {2007},
Bdsk-File-1 = {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}}

• J. Carette and R. Janicki. — Computing properties of numerical imperative programs by symbolic computation. — Fundamenta informaticae, 80.1-3:125-146, 2007.
[BibTeX]
@article{CaretteJanicki2007,
Author = {Carette, J. and Janicki, R.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Fundamenta Informaticae},
Number = {1-3},
Pages = {125-146},
Title = {Computing properties of numerical imperative programs by symbolic computation},
Volume = {80},
Year = {2007}}

• M. Kauers. — Computer algebra and power series with positive coefficients. — Fpsac’07 – 19th international conference on formal power series and algebraic combinatorics, 2007.
[BibTeX]
@inproceedings{Kauers2007,
Author = {Kauers, M.},
Booktitle = {FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:07:30 +0000},
Title = {Computer algebra and power series with positive coefficients},
Year = {2007}}

• L. Kovács, N. Popov, and T. Jebelean. — Combining logic and algebraic techniques for program verification in theorema. — Proceedings – isola 2006: 2nd international symposium on leveraging applications of formal methods, verification and validation, pages 67-74, 2007.
[BibTeX]
@inproceedings{KovacsPopovJebelean2007,
Author = {Kov{\'a}cs, L. and Popov, N. and Jebelean, T.},
Booktitle = {Proceedings - ISoLA 2006: 2nd International Symposium on Leveraging Applications of Formal Methods, Verification and Validation},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {67-74},
Title = {Combining logic and algebraic techniques for program verification in Theorema},
Year = {2007}}

• T. Mansour, M. Schork, and Y. Sun. — Motzkin numbers of higher rank: generating function and explicit expression. — Journal of inequalities in pure and applied mathematics, 8.2: 2007.
[BibTeX]
@article{MansourSchorkSun2007,
Author = {Mansour, T. and Schork, M. and Sun, Y.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Inequalities in Pure and Applied Mathematics},
Number = {2},
Title = {Motzkin numbers of higher rank: Generating function and explicit expression},
Volume = {8},
Year = {2007}}

• D. Zeilberger. — The holonomic ansatz ii. automatic discovery(!) and proof(!!) of holonomic determinant evaluations. — Annals of combinatorics, 11.2:241-247, 2007.
[BibTeX]
@article{Zeilberger2007,
Author = {Zeilberger, D.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Annals of Combinatorics},
Number = {2},
Pages = {241-247},
Title = {The Holonomic Ansatz II. Automatic discovery(!) and proof(!!) of holonomic determinant evaluations},
Volume = {11},
Year = {2007}}

• W. Koepf, P. M. Rajkovic, and S. D. Marinkovic. — Properties of q-holonomic functions. — Journal of difference equations and applications, 13.7:621-638, 2007.
[BibTeX]
@article{KoepfRajkovicMarinkovic2007,
Author = {Koepf, W. and Rajkovic, P. M. and Marinkovic, S. D.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Difference Equations and Applications},
Number = {7},
Pages = {621-638},
Title = {Properties of q-holonomic functions},
Volume = {13},
Year = {2007}}

• W. Koepf. — Bieberbach’s conjecture, the de branges and weinstein functions and the askey-gasper inequality. — Ramanujan journal, 13.1-3:103-129, 2007.
[BibTeX]
@article{Koepf2007,
Author = {Koepf, W.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Ramanujan Journal},
Number = {1-3},
Pages = {103-129},
Title = {Bieberbach's conjecture, the de Branges and Weinstein functions and the Askey-Gasper inequality},
Volume = {13},
Year = {2007}}

• M. Kauers. — An algorithm for deciding zero equivalence of nested polynomially recurrent sequences. — Acm transactions on algorithms, 3.2: 2007.
[BibTeX]
@article{Kauers2007a,
Author = {Kauers, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {ACM Transactions on Algorithms},
Number = {2},
Title = {An algorithm for deciding zero equivalence of nested polynomially recurrent sequences},
Volume = {3},
Year = {2007}}

• C. Schneider. — Apéry’s double sum is plain sailing indeed. — Electronic journal of combinatorics, 14.1 N:1-3, 2007.
[BibTeX]
@article{Schneider2007,
Author = {Schneider, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Journal of Combinatorics},
Number = {1 N},
Pages = {1-3},
Title = {Ap{\'e}ry's double sum is plain sailing indeed},
Volume = {14},
Year = {2007}}

### 2006

• Paolo Massazza and Roberto Radicioni. — A symbolic approach to computing the holonomic functions. — Pure mathematics and applications, 17.1-2:147-164, 2006.
[BibTeX]
@article{MassazzaRadicioni2006,
Author = {Massazza, Paolo and Radicioni, Roberto},
Date-Modified = {2013-03-05 09:26:17 +0000},
Issn = {1218-4586},
Journal = {Pure Mathematics and Applications},
Mrclass = {68W30 (33F10 34A55)},
Mrnumber = {MR2380354 (2008m:68243)},
Number = {1-2},
Pages = {147--164},
Title = {A symbolic approach to computing the holonomic functions},
Volume = {17},
Year = {2006},
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• Mireille Bousquet-M{é}lou. — Rational and algebraic series in combinatorial enumeration. — International Congress of Mathematicians. Vol. III. Eur. Math. Soc., Zürich, 2006. 789-826.
[BibTeX]
@incollection{Bousquet-Melou2006a,
Author = {Bousquet-M{{\'e}}lou, Mireille},
Booktitle = {International {C}ongress of {M}athematicians. {V}ol. {III}},
Date-Modified = {2013-03-05 09:23:08 +0000},
Mrclass = {05A15 (68Q45)},
Mrnumber = {2275707 (2007k:05008)},
Mrreviewer = {Paul Klingsberg},
Pages = {789--826},
Publisher = {Eur. Math. Soc., Z{\"u}rich},
Title = {Rational and algebraic series in combinatorial enumeration},
Year = {2006},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2275707}}

• Mireille Bousquet-Mélou and Guoce Xin. — On partitions avoiding 3-crossings. — Séminaire lotharingien de combinatoire, B54e 1-21, 2006.
[BibTeX]
@article{Bousquet-MelouXin2006,
Author = {Bousquet-M{\'e}lou, Mireille and Xin, Guoce},
Date-Modified = {2013-03-05 09:22:01 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Pages = {1--21},
Title = {On Partitions Avoiding 3-Crossings},
Volume = {B54e},
Year = {2006},
Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8QNy4uLy4uL1NreURyaXZlL0JpYmxpby9hcnRpY2xlL0JvdXNxdWV0LU1lbG91WGluMjAwNi5wZGbSFwsYGVdOUy5kYXRhTxEBzgAAAAABzgACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAzDEvEkgrAAAAHBfPGUJvdXNxdWV0LU1lbG91WGluMjAwNi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAdpZ/HKI+MAAAAAAAAAAAAAgAEAAAJIAAAAAAAAAAAAAAAAAAAAAdhcnRpY2xlAAAQAAgAAMwxEvIAAAARAAgAAMcogXwAAAABABQAHBfPABwXwwDcytgABn1hAAIN+QACAE9NYWNpbnRvc2ggSEQ6VXNlcnM6AHNhbHZ5OgBTa3lEcml2ZToAQmlibGlvOgBhcnRpY2xlOgBCb3VzcXVldC1NZWxvdVhpbjIwMDYucGRmAAAOADQAGQBCAG8AdQBzAHEAdQBlAHQALQBNAGUAbABvAHUAWABpAG4AMgAwADAANgAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAPVVzZXJzL3NhbHZ5L1NreURyaXZlL0JpYmxpby9hcnRpY2xlL0JvdXNxdWV0LU1lbG91WGluMjAwNi5wZGYAABMAAS8AABUAAgAM//8AAIAG0hscHR5aJGNsYXNzbmFtZVgkY2xhc3Nlc11OU011dGFibGVEYXRhox0fIFZOU0RhdGFYTlNPYmplY3TSGxwiI1xOU0RpY3Rpb25hcnmiIiBfEA9OU0tleWVkQXJjaGl2ZXLRJidUcm9vdIABAAgAEQAaACMALQAyADcAQABGAE0AVQBgAGcAagBsAG4AcQBzAHUAdwCEAI4AyADNANUCpwKpAq4CuQLCAtAC1ALbAuQC6QL2AvkDCwMOAxMAAAAAAAACAQAAAAAAAAAoAAAAAAAAAAAAAAAAAAADFQ==}}

• M. Kauers. — Shift equivalence of p-finite sequences. — Electronic journal of combinatorics, 13.1 R:1-16, 2006.
[BibTeX]
@article{Kauers2006,
Author = {Kauers, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Journal of Combinatorics},
Number = {1 R},
Pages = {1-16},
Title = {Shift equivalence of P-finite sequences},
Volume = {13},
Year = {2006}}

• A. Bećirović, P. Paule, V. Pillwein, A. Riese, C. Schneider, and J. Schöberl. — Hypergeometric summation algorithms for high-order finite elements. — Computing (vienna/new york), 78.3:235-249, 2006.
[BibTeX]
@article{BecirovicPaulePillweinRieseSchneiderSchoberl2006,
Author = {Be{\'c}irovi{\'c}, A. and Paule, P. and Pillwein, V. and Riese, A. and Schneider, C. and Sch{\"o}berl, J.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Computing (Vienna/New York)},
Number = {3},
Pages = {235-249},
Title = {Hypergeometric summation algorithms for high-order finite elements},
Volume = {78},
Year = {2006}}

• A. Rechnitzer. — Haruspicy 3: the anisotropic generating function of directed bond-animals is not d-finite. — Journal of combinatorial theory.series a, 113.6:1031-1049, 2006.
[BibTeX]
@article{Rechnitzer2006,
Author = {Rechnitzer, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Combinatorial Theory.Series A},
Number = {6},
Pages = {1031-1049},
Title = {Haruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite},
Volume = {113},
Year = {2006}}

• M. Bousquet-Mélou. — Three osculating walkers. — Journal of physics: conference series, 42.1:35-46, 2006.
[BibTeX]
@article{Bousquet-Melou2006,
Author = {Bousquet-M{\'e}lou, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Physics: Conference Series},
Number = {1},
Pages = {35-46},
Title = {Three osculating walkers},
Volume = {42},
Year = {2006}}

• S. Gerhold and M. Kauers. — A computer proof of turán’s inequality. — Journal of inequalities in pure and applied mathematics, 7.2:1-4, 2006.
[BibTeX]
@article{GerholdKauers2006,
Author = {Gerhold, S. and Kauers, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Inequalities in Pure and Applied Mathematics},
Number = {2},
Pages = {1-4},
Title = {A computer proof of Tur{\'a}n's inequality},
Volume = {7},
Year = {2006}}

• T. C. Scott, M. Aubert-Frécon, and J. Grotendorst. — New approach for the electronic energies of the hydrogen molecular ion. — Chemical physics, 324.2-3:323-338, 2006.
[BibTeX]
@article{ScottAubert-FreconGrotendorst2006,
Author = {Scott, T. C. and Aubert-Fr{\'e}con, M. and Grotendorst, J.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Chemical Physics},
Number = {2-3},
Pages = {323-338},
Title = {New approach for the electronic energies of the hydrogen molecular ion},
Volume = {324},
Year = {2006}}

### 2005

• E. Fusy. — Counting unrooted maps using tree-decomposition. — Fpsac proceedings 2005 – 17th annual international conference on formal power series and algebraic combinatorics, pages 123-134, 2005.
[BibTeX]
@inproceedings{Fusy2005,
Author = {Fusy, E.},
Booktitle = {FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {123-134},
Title = {Counting unrooted maps using tree-decomposition},
Year = {2005}}

• B. Salvy. — D-finiteness: algorithms and applications. — Proceedings of the international symposium on symbolic and algebraic computation, issac, pages 2-3, 2005.
[BibTeX]
@inproceedings{Salvy2005,
Author = {Salvy, B.},
Booktitle = {Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {2-3},
Title = {D-finiteness: Algorithms and applications},
Volume = {2005},
Year = {2005}}

• M. Bodirsky, C. Gröpl, D. Johannsen, and M. Kang. — A direct decomposition of 3-connected planar graphs. — Fpsac proceedings 2005 – 17th annual international conference on formal power series and algebraic combinatorics, pages 459-470, 2005.
[BibTeX]
@inproceedings{BodirskyGroplJohannsenKang2005,
Author = {Bodirsky, M. and Gr{\"o}pl, C. and Johannsen, D. and Kang, M.},
Booktitle = {FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {459-470},
Title = {A direct decomposition of 3-connected planar graphs},
Year = {2005}}

• F. Chyzak, M. Mishna, and B. Salvy. — Effective scalar products of d-finite symmetric functions. — Journal of combinatorial theory.series a, 112.1:1-43, 2005.
[BibTeX]
@article{ChyzakMishnaSalvy2005,
Author = {Chyzak, F. and Mishna, M. and Salvy, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Combinatorial Theory.Series A},
Number = {1},
Pages = {1-43},
Title = {Effective scalar products of D-finite symmetric functions},
Volume = {112},
Year = {2005}}

• M. Bousquet-Mélou. — Algebraic generating functions in enumerative combinatorics and context-free languages. — Lecture notes in computer science, pages 18-35, 2005.
[BibTeX]
@inproceedings{Bousquet-Melou2005,
Author = {Bousquet-M{\'e}lou, M.},
Booktitle = {Lecture Notes in Computer Science},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {18-35},
Title = {Algebraic generating functions in enumerative combinatorics and context-free languages},
Volume = {3404},
Year = {2005}}

• F. Ulmer. — Note on algebraic solutions of differential equations with known finite galois group. — Applicable algebra in engineering, communications and computing, 16.4:205-218, 2005.
[BibTeX]
@article{Ulmer2005,
Author = {Ulmer, F.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Applicable Algebra in Engineering, Communications and Computing},
Number = {4},
Pages = {205-218},
Title = {Note on algebraic solutions of differential equations with known finite Galois group},
Volume = {16},
Year = {2005}}

• G. E. Andrews, P. Paule, and C. Schneider. — Plane partitions vi: stembridge’s tspp theorem. — Advances in applied mathematics, 34.4 SPEC. ISS.:709-739, 2005.
[BibTeX]
@article{AndrewsPauleSchneider2005,
Author = {Andrews, G. E. and Paule, P. and Schneider, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Advances in Applied Mathematics},
Number = {4 SPEC. ISS.},
Pages = {709-739},
Title = {Plane partitions VI: Stembridge's TSPP theorem},
Volume = {34},
Year = {2005}}

### 2004

• C. Schneider. — The summation package sigma: underlying principles and a rhombus tiling application. — Discrete mathematics and theoretical computer science, 6.2:365-386, 2004.
[BibTeX]
@article{Schneider2004,
Author = {Schneider, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Discrete Mathematics and Theoretical Computer Science},
Number = {2},
Pages = {365-386},
Title = {The summation package Sigma: Underlying principles and a rhombus tiling application},
Volume = {6},
Year = {2004}}

• M. Ahmed, R. Ward, and N. Kharma. — Solving mathematical problems using knowledge-based systems. — Mathematics and computers in simulation, 67.1-2:149-161, 2004.
[BibTeX]
@article{AhmedWardKharma2004,
Author = {Ahmed, M. and Ward, R. and Kharma, N.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Mathematics and Computers in Simulation},
Number = {1-2},
Pages = {149-161},
Title = {Solving mathematical problems using knowledge-based systems},
Volume = {67},
Year = {2004}}

• M. Foupouagnigni, W. Koepf, and A. Ronveaux. — Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials. — Journal of computational and applied mathematics, 162.2:299-326, 2004.
[BibTeX]
@article{FoupouagnigniKoepfRonveaux2004,
Author = {Foupouagnigni, M. and Koepf, W. and Ronveaux, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Computational and Applied Mathematics},
Number = {2},
Pages = {299-326},
Title = {Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials},
Volume = {162},
Year = {2004}}

### 2003

• N. J. A. Sloane. — The on-line encyclopedia of integer sequences. — Notices of the ams, 50.8:912-915, 2003.
[BibTeX]
@article{Sloane2003,
Author = {Sloane, N. J. A.},
Coden = {AMNOAN},
Date-Modified = {2013-03-05 09:31:24 +0000},
Issn = {0002-9920},
Journal = {Notices of the AMS},
Mrclass = {11Y55 (05-00 11-00 11B83)},
Mrnumber = {MR1992789 (2004f:11151)},
Mrreviewer = {Christian Krattenthaler},
Number = {8},
Pages = {912--915},
Title = {The on-line encyclopedia of integer sequences},
Volume = {50},
Year = {2003},
Bdsk-File-1 = {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}}

• Wolfram Koepf. — Computer algebra algorithms for orthogonal polynomials and special functions. — Orthogonal polynomials and special functions (Leuven, 2002). Vol. 1817. Lecture Notes in Math.. Berlin: Springer, 2003. 1-24.
doi:10.1007/3-540-44945-0_1
[BibTeX] [PDF]
@incollection{Koepf2003,
Author = {Koepf, Wolfram},
Booktitle = {Orthogonal polynomials and special functions ({L}euven, 2002)},
Date-Modified = {2013-03-05 09:30:57 +0000},
Doi = {10.1007/3-540-44945-0_1},
Mrclass = {33F10 (33C45 33D45 68W30)},
Mrnumber = {2022851 (2004k:33046)},
Pages = {1--24},
Publisher = {Springer},
Series = {Lecture Notes in Math.},
Title = {Computer algebra algorithms for orthogonal polynomials and special functions},
Url = {http://dx.doi.org/10.1007/3-540-44945-0_1},
Volume = {1817},
Year = {2003},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2022851}}

• Moulay Barkatou, Frédéric Chyzak, and Michèle Loday-Richaud. — Remarques algorithmiques liées au rang d’un opérateur différentiel linéaire. — From combinatorics to dynamical systems (journées de calcul formel, strasbourg, march 22-23, 2002), Eds. F. Fauvet and C. Mitschi. de Gruyter, pages 87—129, 2003.
[BibTeX] [Abstract] In French. ISBN 3-11-017875-3
(French) Dans cet article nous décrivons et comparons différentes méthodes algorithmiques pour résoudre le problème suivant : étant donnée une série hat f(x)= sum m geq 0umxm solution d’une équation différentielle linéaire ordinaire et un nombre entier r>0, construire une équation différentielle vérifiée par les sous-séries hat fj(x)= sum m geq 0uj+mrxj+mr de ses termes de r en r. Cette question appara{\^\i} t naturellement lors de l’implantation en calcul formel des solutions formelles et de leurs (multi-)sommes. Les méthodes proposées sont implantées en sc Maple et nous donnons l’adresse des programmes correspondants.En appendice nous indiquons une démarche constructive réaliste pour le calcul effectif des invariants formels d’une équation ou d’un système. (English) This paper aims at introducing and comparing various methods for solving the following problem which arises naturally in computer algebra for differential equations: given a series hat f(x)= sum m geq 0umxm solution of an ordinary linear differential equation and given an integer r geq 2 find a differential equation satisfied by the sub-series hat fj(x)= sum _m geq 0uj+mrxj+mr. These methods have been implemented in sc Maple. References are given to the corresponding programs. Possible realistic algorithms to effectively calculate the formal invariants of an ordinary linear differential system of order one and arbitrary rank are sketched in an Appendix.

@inproceedings{BarkatouChyzakLoday-Richaud2003,
Author = {Barkatou, Moulay and Chyzak, Fr{\'e}d{\'e}ric and Loday-Richaud, Mich{\e}le},
Booktitle = {From Combinatorics to Dynamical Systems (Journ{\'e}es de Calcul Formel, Strasbourg, March 22-23, 2002)},
Date-Modified = {2013-03-05 09:29:10 +0000},
Editor = {Fauvet, F. and Mitschi, C.},
Note = {In French. ISBN 3-11-017875-3},
Pages = {87---129},
Publisher = {de Gruyter},
Series = {IRMA Lectures in Mathematics and Theoretical Physics},
Title = {Remarques algorithmiques li{\'e}es au rang d'un op{\'e}rateur diff{\'e}rentiel lin{\'e}aire},
Volume = {3},
Web-Comment = {Preliminary version (Univ. Angers Research Report #164).},
Year = {2003},
Abstract = {(French) Dans cet article nous d{\'e}crivons et comparons
diff{\'e}rentes m{\'e}thodes algorithmiques pour r{\'e}soudre le probl{\e}me suivant
: {\'e}tant donn{\'e}e une s{\'e}rie hat f(x)= sum m geq 0umxm solution
d'une {\'e}quation diff{\'e}rentielle lin{\'e}aire ordinaire et un nombre
entier r>0, construire une {\'e}quation diff{\'e}rentielle v{\'e}rifi{\'e}e par les
sous-s{\'e}ries hat fj(x)= sum m geq 0uj+mrxj+mr de ses termes de
r en r. Cette question appara{\^\i} t naturellement lors de l'implantation
en calcul formel des solutions formelles et de leurs (multi-)sommes. Les
m{\'e}thodes propos{\'e}es sont implant{\'e}es en sc Maple et nous donnons
l'adresse des programmes correspondants.En appendice nous indiquons une
d{\'e}marche constructive r{\'e}aliste pour le calcul effectif des invariants
formels d'une {\'e}quation ou d'un syst{\e}me. (English) This paper aims at
introducing and comparing various methods for solving the following problem
which arises naturally in computer algebra for differential equations: given
a series hat f(x)= sum m geq 0umxm solution of an ordinary linear
differential equation and given an integer r geq 2 find a differential
equation satisfied by the sub-series hat fj(x)= sum _m geq
0uj+mrxj+mr. These methods have been implemented in sc Maple.
References are given to the corresponding programs. Possible realistic
algorithms to effectively calculate the formal invariants of an ordinary
linear differential system of order one and arbitrary rank are sketched in an
Appendix.}}

• C. A. C. Brennan and H. Prodinger. — The pills problem revisited. — Quaestiones mathematicae, 26.4:427-439, 2003.
[BibTeX]
@article{BrennanProdinger2003,
Author = {Brennan, C. A. C. and Prodinger, H.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Quaestiones Mathematicae},
Number = {4},
Pages = {427-439},
Title = {The pills problem revisited},
Volume = {26},
Year = {2003}}

• L. Meunier and B. Salvy. — Esf: an automatically generated encyclopedia of special functions. — Proceedings of the international symposium on symbolic and algebraic computation, issac, pages 199-206, 2003.
[BibTeX]
@inproceedings{MeunierSalvy2003,
Author = {Meunier, L. and Salvy, B.},
Booktitle = {Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC},
Date-Modified = {2013-03-05 09:07:30 +0000},
Pages = {199-206},
Title = {ESF: An Automatically Generated Encyclopedia of Special Functions},
Year = {2003}}

• M. Foupouagnigni, W. Koepf, and A. Ronveaux. — On fourth-order difference equations for orthogonal polynomials of a discrete variable: derivation, factorization and solutions. — Journal of difference equations and applications, 9.9:777-804, 2003.
[BibTeX]
@article{FoupouagnigniKoepfRonveaux2003,
Author = {Foupouagnigni, M. and Koepf, W. and Ronveaux, A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Difference Equations and Applications},
Number = {9},
Pages = {777-804},
Title = {On fourth-order difference equations for orthogonal polynomials of a discrete variable: Derivation, factorization and solutions},
Volume = {9},
Year = {2003}}

• P. Paule and C. Schneider. — Computer proofs of a new family of harmonic number identities. — Advances in applied mathematics, 31.2:359-378, 2003.
[BibTeX]
@article{PauleSchneider2003,
Author = {Paule, P. and Schneider, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Advances in Applied Mathematics},
Number = {2},
Pages = {359-378},
Title = {Computer proofs of a new family of harmonic number identities},
Volume = {31},
Year = {2003}}

• M. Durand. — Asymptotic analysis of an optimized quicksort algorithm. — Information processing letters, 85.2:73-77, 2003.
[BibTeX]
@article{Durand2003,
Author = {Durand, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Information Processing Letters},
Number = {2},
Pages = {73-77},
Title = {Asymptotic analysis of an optimized quicksort algorithm},
Volume = {85},
Year = {2003}}

### 2002

• Anthony J. Guttmann and Markus Vöge. — Lattice paths: vicious walkers and friendly walkers. — Journal of statistical planning and inference, 101.1-2:107-131, 2002.
doi:DOI: 10.1016/S0378-3758(01)00158-6
[BibTeX] [Abstract] [PDF]
We introduce a model of friendly walkers which generalises the well-known vicious walker model. Friendly walkers refers to a model in which any number P of directed lattice paths, starting at adjacent lattice sites, simultaneously proceed in one of the allowed lattice directions. In the case of n-friendly walkers the paths may stay together for n vertices. The previously considered case of vicious walkers corresponds to the case n=0. The Gessel-Viennot theorem applies only to vicious walkers, and not to the cases n>0. The connection between this model and the m-vertex models of Statistical Mechanics is described. For planar configurations, we solve the two-walker case for all n. Conjectured solutions for the three-walker case with n=1 are also obtained. Numerical studies lead to the conjectured asymptotic behaviour for all n, for an arbitrary number of walkers P and in arbitrary spatial dimension d[greater-or-equal, slanted]2.

@article{GuttmannVoge2002,
Author = {Guttmann, Anthony J. and V{\"o}ge, Markus},
Date-Modified = {2013-03-05 09:32:03 +0000},
Doi = {DOI: 10.1016/S0378-3758(01)00158-6},
Issn = {0378-3758},
Journal = {Journal of Statistical Planning and Inference},
Keywords = {Vertex model},
Number = {1-2},
Pages = {107 - 131},
Title = {Lattice paths: vicious walkers and friendly walkers},
Url = {http://www.sciencedirect.com/science/article/B6V0M-44VDYR3-C/2/f6af3d7edda125a5d25b97219148be0c},
Volume = {101},
Year = {2002},
Abstract = {
We introduce a model of friendly walkers which generalises the well-known vicious walker model. Friendly walkers refers to a model in which any number P of directed lattice paths, starting at adjacent lattice sites, simultaneously proceed in one of the allowed lattice directions. In the case of n-friendly walkers the paths may stay together for n vertices. The previously considered case of vicious walkers corresponds to the case n=0. The Gessel-Viennot theorem applies only to vicious walkers, and not to the cases n>0. The connection between this model and the m-vertex models of Statistical Mechanics is described. For planar configurations, we solve the two-walker case for all n. Conjectured solutions for the three-walker case with n=1 are also obtained. Numerical studies lead to the conjectured asymptotic behaviour for all n, for an arbitrary number of walkers P and in arbitrary spatial dimension d[greater-or-equal, slanted]2.},
Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V0M-44VDYR3-C/2/f6af3d7edda125a5d25b97219148be0c},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0378-3758(01)00158-6}}

• J. Van der Hoeven. — Relax, but don’t be too lazy. — Journal of symbolic computation, 34.6:479-542, 2002.
[BibTeX]
@article{Van-der-Hoeven2002,
Author = {Van der Hoeven, J.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {6},
Pages = {479-542},
Title = {Relax, but don't be too lazy},
Volume = {34},
Year = {2002}}

• P. Flajolet, K. Hatzis, S. Nikoletseas, and P. Spirakis. — On the robustness of interconnections in random graphs: a symbolic approach. — Theoretical computer science, 287.2:515-534, 2002.
[BibTeX]
@article{FlajoletHatzisNikoletseasSpirakis2002,
Author = {Flajolet, P. and Hatzis, K. and Nikoletseas, S. and Spirakis, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {2},
Pages = {515-534},
Title = {On the robustness of interconnections in random graphs: A symbolic approach},
Volume = {287},
Year = {2002}}

• P. Nicodème, B. Salvy, and P. Flajolet. — Motif statistics. — Theoretical computer science, 287.2:593-617, 2002.
[BibTeX]
@article{NicodemeSalvyFlajolet2002,
Author = {Nicod{\e}me, P. and Salvy, B. and Flajolet, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {2},
Pages = {593-617},
Title = {Motif statistics},
Volume = {287},
Year = {2002}}

• B. R. Fabijonas. — Laplace’s method on a computer algebra system with an application to the real valued modified bessel functions. — Journal of computational and applied mathematics, 146.2:323-342, 2002.
[BibTeX]
@article{Fabijonas2002,
Author = {Fabijonas, B. R.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Computational and Applied Mathematics},
Number = {2},
Pages = {323-342},
Title = {Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions},
Volume = {146},
Year = {2002}}

• E. Deutsch and M. Noy. — Statistics on non-crossing trees. — Discrete mathematics, 254.1-3:75-87, 2002.
[BibTeX]
@article{DeutschNoy2002,
Author = {Deutsch, E. and Noy, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Discrete Mathematics},
Number = {1-3},
Pages = {75-87},
Title = {Statistics on non-crossing trees},
Volume = {254},
Year = {2002}}

• C. Banderier and P. Flajolet. — Basic analytic combinatorics of directed lattice paths. — Theoretical computer science, 281.1-2:37-80, 2002.
[BibTeX]
@article{BanderierFlajolet2002,
Author = {Banderier, C. and Flajolet, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {1-2},
Pages = {37-80},
Title = {Basic analytic combinatorics of directed lattice paths},
Volume = {281},
Year = {2002}}

### 2001

• B. Beckermann and G. Labahn. — Fraction-free computation of matrix rational interpolants and matrix gcds. — Siam journal on matrix analysis and applications, 22.1:114-144, 2001.
[BibTeX]
@article{BeckermannLabahn2001,
Author = {Beckermann, B. and Labahn, G.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {SIAM Journal on Matrix Analysis and Applications},
Number = {1},
Pages = {114-144},
Title = {Fraction-free computation of matrix rational interpolants and matrix GCDs},
Volume = {22},
Year = {2001}}

### 2000

• Emeric Deutsch and Marc Noy. — New statistics on non-crossing trees. — Formal power series and algebraic combinatorics (Moscow, 2000). Berlin: Springer, 2000. 667-676.
[BibTeX]
@incollection{DeutschNoy2000,
Author = {Deutsch, Emeric and Noy, Marc},
Booktitle = {Formal power series and algebraic combinatorics ({M}oscow, 2000)},
Date-Modified = {2013-03-05 09:34:21 +0000},
Mrclass = {05C05 (05C10)},
Mrnumber = {1798261 (2002c:05051)},
Mrreviewer = {J. Lauri},
Pages = {667--676},
Publisher = {Springer},
Title = {New statistics on non-crossing trees},
Year = {2000},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1798261}}

• Susanna Brogelli, Donatella Merlini, and Renzo Sprugnoli. — Proving a class of hypergeometric identities by means of generating functions. — Formal power series and algebraic combinatorics (Moscow, 2000). Berlin: Springer, 2000. 645-654.
[BibTeX]
@incollection{BrogelliMerliniSprugnoli2000,
Author = {Brogelli, Susanna and Merlini, Donatella and Sprugnoli, Renzo},
Booktitle = {Formal power series and algebraic combinatorics ({M}oscow, 2000)},
Date-Modified = {2013-03-05 09:33:30 +0000},
Mrclass = {33C05 (05A15 33F10)},
Mrnumber = {1798259 (2002d:33005)},
Mrreviewer = {Axel Riese},
Pages = {645--654},
Publisher = {Springer},
Title = {Proving a class of hypergeometric identities by means of generating functions},
Year = {2000},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1798259}}

• F. Bergeron and F. Gascon. — Counting young tableaux of bounded height. — Journal of integer sequences, 3.1:1-7, 2000.
[BibTeX]
@article{BergeronGascon2000,
Author = {Bergeron, F. and Gascon, F.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Integer Sequences},
Number = {1},
Pages = {1-7},
Title = {Counting young tableaux of bounded height},
Volume = {3},
Year = {2000}}

• R. Suter. — Two analogues of a classical sequence. — Journal of integer sequences, 3.1:1-18, 2000.
[BibTeX]
@article{Suter2000,
Author = {Suter, R.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Integer Sequences},
Number = {1},
Pages = {1-18},
Title = {Two analogues of a classical sequence},
Volume = {3},
Year = {2000}}

• B. Beckermann and G. Labahn. — Effective computation of rational approximants and interpolants. — Reliable computing, 6.4:365-390, 2000.
[BibTeX]
@article{BeckermannLabahn2000,
Author = {Beckermann, B. and Labahn, G.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Reliable Computing},
Number = {4},
Pages = {365-390},
Title = {Effective Computation of Rational Approximants and Interpolants},
Volume = {6},
Year = {2000}}

• M. Bousquet-Mélou. — Sorted and/or sortable permutations. — Discrete mathematics, 225.1-3:25-50, 2000.
[BibTeX]
@article{Bousquet-Melou2000,
Author = {Bousquet-M{\'e}lou, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Discrete Mathematics},
Number = {1-3},
Pages = {25-50},
Title = {Sorted and/or sortable permutations},
Volume = {225},
Year = {2000}}

• M. Fulmek and C. Krattenthaler. — The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, ii. — European journal of combinatorics, 21.5:601-640, 2000.
[BibTeX]
@article{FulmekKrattenthaler2000,
Author = {Fulmek, M. and Krattenthaler, C.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {European Journal of Combinatorics},
Number = {5},
Pages = {601-640},
Title = {The Number of Rhombus Tilings of a Symmetric Hexagon which Contain a Fixed Rhombus on the Symmetry Axis, II},
Volume = {21},
Year = {2000}}

• B. Litow. — On hadamard square roots of unity. — Theoretical computer science, 237.1-2:447-454, 2000.
[BibTeX]
@article{Litow2000,
Author = {Litow, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {1-2},
Pages = {447-454},
Title = {On Hadamard square roots of unity},
Volume = {237},
Year = {2000}}

• R. Lercier and F. Morain. — Computing isogenies between elliptic curves over fp n using couveignes’s algorithm. — Mathematics of computation, 69.229:351-370, 2000.
[BibTeX]
@article{LercierMorain2000,
Author = {Lercier, R. and Morain, F.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Mathematics of Computation},
Number = {229},
Pages = {351-370},
Title = {Computing isogenies between elliptic curves over Fp n using Couveignes's algorithm},
Volume = {69},
Year = {2000}}

### 1999

• A. Ronveaux, A. Zarzo, I. Area, and E. Godoy. — Decomposition of polynomials with respect to the cyclic group of order $m$. — J. symbolic comput., 28.6:755-765, 1999.
doi:10.1006/jsco.1999.0337
[BibTeX] Orthogonal polynomials and computer algebra [PDF]
@article{RonveauxZarzoAreaGodoy1999,
Author = {Ronveaux, A. and Zarzo, A. and Area, I. and Godoy, E.},
Date-Modified = {2013-03-05 09:36:30 +0000},
Doi = {10.1006/jsco.1999.0337},
Fjournal = {Journal of Symbolic Computation},
Issn = {0747-7171},
Journal = {J. Symbolic Comput.},
Mrclass = {33F10 (42C05)},
Mrnumber = {1750544 (2001e:33011)},
Mrreviewer = {Pascal Maroni},
Note = {Orthogonal polynomials and computer algebra},
Number = {6},
Pages = {755--765},
Title = {Decomposition of polynomials with respect to the cyclic group of order {$m$}},
Url = {http://dx.doi.org/10.1006/jsco.1999.0337},
Volume = {28},
Year = {1999},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1750544}}

• C. Krattenthaler. — Advanced determinant calculus. — Séminaire lotharingien de combinatoire, 42 1-67, 1999.
[BibTeX]
@article{Krattenthaler1999,
Author = {Krattenthaler, C.},
Date-Modified = {2013-03-05 09:35:19 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Pages = {1--67},
Volume = {42},
Year = {1999},
Bdsk-File-1 = {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}}

• W. Koepf. — Software for the algorithmic work with orthogonal polynomials and special functions. — Electronic transactions on numerical analysis, 9 77-101, 1999.
[BibTeX]
@article{Koepf1999,
Author = {Koepf, W.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Transactions on Numerical Analysis},
Pages = {77-101},
Title = {Software for the algorithmic work with orthogonal polynomials and special functions},
Volume = {9},
Year = {1999}}

• F. Chyzak, I. Gutman, and P. Paule. — Predicting the number of hexagonal systems with 24 and 25 hexagons. — Match, 40 139-151, 1999.
[BibTeX]
@article{ChyzakGutmanPaule1999,
Author = {Chyzak, F. and Gutman, I. and Paule, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Match},
Pages = {139-151},
Title = {Predicting the number of hexagonal systems with 24 and 25 hexagons},
Volume = {40},
Year = {1999}}

• R. Evans, H. D. L. Hollmann, C. Krattenthaler, and Q. Xiang. — Gauss sums, jacobi sums, and p-ranks of cyclic difference sets. — Journal of combinatorial theory.series a, 87.1:74-119, 1999.
[BibTeX]
@article{EvansHollmannKrattenthalerXiang1999,
Author = {Evans, R. and Hollmann, H. D. L. and Krattenthaler, C. and Xiang, Q.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Combinatorial Theory.Series A},
Number = {1},
Pages = {74-119},
Title = {Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets},
Volume = {87},
Year = {1999}}

• P. Flajolet and M. Noy. — Analytic combinatorics of non-crossing configurations. — Discrete mathematics, 204.1-3:203-229, 1999.
[BibTeX]
@article{FlajoletNoy1999,
Author = {Flajolet, P. and Noy, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Discrete Mathematics},
Number = {1-3},
Pages = {203-229},
Title = {Analytic combinatorics of non-crossing configurations},
Volume = {204},
Year = {1999}}

• A. Denise and P. Zimmermann. — Uniform random generation of decomposable structures using floating-point arithmetic. — Theoretical computer science, 218.2:233-248, 1999.
[BibTeX]
@article{DeniseZimmermann1999,
Author = {Denise, A. and Zimmermann, P.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Theoretical Computer Science},
Number = {2},
Pages = {233-248},
Title = {Uniform random generation of decomposable structures using floating-point arithmetic},
Volume = {218},
Year = {1999}}

### 1998

• C. Krattenthaler. — An alternative evaluation of the Andrews-Burge determinant. — Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996). Vol. 161. Progr. Math.. Boston, MA: Birkhäuser Boston, 1998. 263-270.
[BibTeX]
@incollection{Krattenthaler1998,
Author = {Krattenthaler, C.},
Booktitle = {Mathematical essays in honor of {G}ian-{C}arlo {R}ota ({C}ambridge, {MA}, 1996)},
Date-Modified = {2013-03-05 09:38:08 +0000},
Mrclass = {05A19 (05A10 33C20)},
Mrnumber = {1627323 (99g:05011)},
Mrreviewer = {George E. Andrews},
Pages = {263--270},
Publisher = {Birkh{\"a}user Boston},
Series = {Progr. Math.},
Title = {An alternative evaluation of the {A}ndrews-{B}urge determinant},
Volume = {161},
Year = {1998},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1627323}}

• Alain Denise, Isabelle Dutour, and Paul Zimmermann. — Cs: a mupad package for counting and randomly generating combinatorial structures. — Formal power series and algebraic combinatorics, pages 1-10, 1998.
[BibTeX] [PDF]
@inproceedings{DeniseDutourZimmerman1998,
Author = {Denise, Alain and Dutour, Isabelle and Zimmermann, Paul},
Booktitle = {Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2013-03-05 09:37:01 +0000},
Pages = {1--10},
Title = {CS: a MuPAD Package for Counting and Randomly Generating Combinatorial Structures},
Url = {http://www.fpsac.org/FPSAC98/articles.html},
Year = {1998},
Bdsk-File-1 = {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}}

• A. Panholzer and H. Prodinger. — Towards a more precise analysis of an algorithm to generate binary trees: a tutorial. — Computer journal, 41.3:201-204, 1998.
[BibTeX]
@article{PanholzerProdinger1998,
Author = {Panholzer, A. and Prodinger, H.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Computer journal},
Number = {3},
Pages = {201-204},
Title = {Towards a More Precise Analysis of an Algorithm to Generate Binary Trees: A Tutorial},
Volume = {41},
Year = {1998}}

• M. Bousquet-Mélou. — Multi-statistic enumeration of two-stack sortable permutations. — Electronic journal of combinatorics, 5.1: 1998.
[BibTeX]
@article{Bousquet-Melou1998,
Author = {Bousquet-M{\'e}lou, M.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Journal of Combinatorics},
Number = {1},
Title = {Multi-statistic enumeration of two-stack sortable permutations},
Volume = {5},
Year = {1998}}

• C. Mart{‘i}nez, A. Panholzer, and H. Prodinger. — On the number of descendants and ascendants in random search trees. — Electronic journal of combinatorics, 5.1: 1998.
[BibTeX]
@article{MartinezPanholzerProdinger1998,
Author = {Mart{\'\i}nez, C. and Panholzer, A. and Prodinger, H.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Electronic Journal of Combinatorics},
Number = {1},
Title = {On the number of descendants and ascendants in random search trees},
Volume = {5},
Year = {1998}}

• F. Chyzak and B. Salvy. — Non-commutative elimination in ore algebras proves multivariate identities. — Journal of symbolic computation, 26.2:187-227, 1998.
[BibTeX]
@article{ChyzakSalvy1998,
Author = {Chyzak, F. and Salvy, B.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Journal of Symbolic Computation},
Number = {2},
Pages = {187-227},
Title = {Non-commutative elimination in ore algebras proves multivariate identities},
Volume = {26},
Year = {1998}}

### 1997

• S. P. Tsarev. — Symbolic manipulation of integrodifferential expressions and factorization of linear ordinary differential operators over transcendental extensions of a differential field. — Issac ’97: proceedings of the 1997 international symposium on symbolic and algebraic computation, New York, NY, USA: ACM, pages 310-315, 1997.
doi:http://doi.acm.org/10.1145/258726.258824
[BibTeX]
@inproceedings{Tsarev1997,
Address = {New York, NY, USA},
Author = {Tsarev, S. P.},
Booktitle = {ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation},
Date-Modified = {2013-03-05 09:43:45 +0000},
Doi = {http://doi.acm.org/10.1145/258726.258824},
Isbn = {0-89791-875-4},
Location = {Kihei, Maui, Hawaii, United States},
Pages = {310--315},
Publisher = {ACM},
Title = {Symbolic manipulation of integrodifferential expressions and factorization of linear ordinary differential operators over transcendental extensions of a differential field},
Year = {1997},
Bdsk-Url-1 = {http://doi.acm.org/10.1145/258726.258824}}

• Helmut Prodinger. — On a question of Cooper and Kennedy. — Fibonacci quart., 35.2:135-136, 1997.
[BibTeX]
@article{Prodinger1997,
Author = {Prodinger, Helmut},
Coden = {FIBQAU},
Date-Modified = {2013-03-05 09:43:26 +0000},
Fjournal = {The Fibonacci Quarterly. The Official Journal of the Fibonacci Association},
Issn = {0015-0517},
Journal = {Fibonacci Quart.},
Mrclass = {11B37},
Mrnumber = {1448026 (98d:11016)},
Mrreviewer = {Antal Balog},
Number = {2},
Pages = {135--136},
Title = {On a question of {C}ooper and {K}ennedy},
Volume = {35},
Year = {1997},
Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1448026}}

• Ziming Li and István Nemes. — A modular algorithm for computing greatest common right divisors of ore polynomials. — Issac ’97: proceedings of the 1997 international symposium on symbolic and algebraic computation, Ed. Wolfgang W. Küchlin. New York, NY, USA: ACM Press, pages 282-289, 1997.
doi:doi.acm.org/10.1145/258726.258812
[BibTeX]
@inproceedings{LiNemes1997,
Address = {New York, NY, USA},
Author = {Li, Ziming and Nemes, Istv{\'a}n},
Booktitle = {ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation},
Date-Modified = {2013-03-05 09:42:39 +0000},
Doi = {doi.acm.org/10.1145/258726.258812},
Editor = {K{\"u}chlin, Wolfgang W.},
Isbn = {0-89791-875-4},
Location = {Kihei, Maui, Hawaii, United States},
Pages = {282--289},
Publisher = {ACM Press},
Title = {A modular algorithm for computing greatest common right divisors of Ore polynomials},
Year = {1997},
Bdsk-Url-1 = {http://dx.doi.org/10.1145/258726.258812}}

• Philippe Flajolet and Bruno Salvy. — The Sigsam challenges: symbolic asymptotics in practice. — Sigsam bulletin, 31.4:36-47, 1997.
doi:10.1145/274888.274890
[BibTeX] [Abstract]
We present answers to 5 out of 10 of the “Problems, Puzzles, Challenges” proposed by G. J. Fee and M. B. Monagan in the March 1997 issue of the Sigsam Bulletin. In all cases, the answer to a seemingly numerical problem is obtained via series expansions and asymptotic methods. This illustrates more generally the crucial role played in the presence of singular behaviours by symbolic asymptotics as a bridge between symbolic computation and numerical computations. All our computations have been performed using MapleV.4 on a Dec Alpha (255/233). The timings indicated correspond to executions on this machine.

@article{FlajoletSalvy1997,
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Modified = {2013-03-05 09:42:21 +0000},
Doi = {10.1145/274888.274890},
Journal = {SIGSAM Bulletin},
Month = dec,
Number = 4,
Pages = {36--47},
Title = {The {S}IGSAM Challenges: Symbolic Asymptotics in Practice},
Volume = 31,
Year = 1997,
Abstract = {We present answers to 5 out of 10 of the Problems, Puzzles, Challenges'' proposed by G. J. Fee and M. B. Monagan in the March 1997 issue of the Sigsam Bulletin. In all cases, the answer to a seemingly numerical problem is obtained via series expansions and asymptotic methods. This illustrates more generally the crucial role played in the presence of singular behaviours by symbolic asymptotics as a bridge between symbolic computation and numerical computations. All our computations have been performed using MapleV.4 on a Dec Alpha (255/233). The timings indicated correspond to executions on this machine.},
Bdsk-Url-1 = {http://dx.doi.org/10.1145/274888.274890}}

• Mireille Bousquet-Mélou and Anthony J. Guttmann. — Enumeration of three-dimensional convex polygons. — Annals of combinatorics, 1.1:27-53, 1997.
[BibTeX]
@article{Bousquet-MelouGuttmann1997,
Author = {Bousquet-M{\'e}lou, Mireille and Guttmann, Anthony J.},
Date-Modified = {2013-03-05 09:42:06 +0000},
Journal = {Annals of Combinatorics},
Number = {1},
Pages = {27--53},
Title = {Enumeration of Three-dimensional Convex Polygons},
Volume = 1,
Year = 1997,
Bdsk-File-1 = {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}}

• Sergei A. Abramov and Eugene V. Zima. — Minimal completely factorable annihilators. — Issac ’97: proceedings of the 1997 international symposium on symbolic and algebraic computation, New York, NY, USA: ACM, pages 290-297, 1997.
doi:http://doi.acm.org/10.1145/258726.258815
[BibTeX]
@inproceedings{AbramovZima1997,
Address = {New York, NY, USA},
Author = {Abramov, Sergei A. and Zima, Eugene V.},
Booktitle = {ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation},
Date-Modified = {2013-03-05 09:39:44 +0000},
Doi = {http://doi.acm.org/10.1145/258726.258815},
Isbn = {0-89791-875-4},
Location = {Kihei, Maui, Hawaii, United States},
Pages = {290--297},
Publisher = {ACM},
Title = {Minimal completely factorable annihilators},
Year = {1997},
Bdsk-Url-1 = {http://doi.acm.org/10.1145/258726.258815}}

• R. B. Pelz and Y. Gulak. — Evidence for a real-time singularity in hydrodynamics from time series analysis. — Physical review letters, 79.25:4998-5001, 1997.
[BibTeX]
@article{PelzGulak1997,
Author = {Pelz, R. B. and Gulak, Y.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Physical Review Letters},
Number = {25},
Pages = {4998-5001},
Title = {Evidence for a real-time singularity in hydrodynamics from time series analysis},
Volume = {79},
Year = {1997}}

• W. Koepf. — Identities for families of orthogonal polynomials and special functions. — Integral transforms and special functions, 5.1-2:69-102, 1997.
[BibTeX]
@article{Koepf1997,
Author = {Koepf, W.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Integral Transforms and Special Functions},
Number = {1-2},
Pages = {69-102},
Title = {Identities for families of orthogonal polynomials and special functions},
Volume = {5},
Year = {1997}}

### 1996

• Doron Zeilberger. — Self-avoiding walks, the language of science, and fibonacci numbers. — Journal of statistical planning and inference, 54.1:135-138, 1996.
doi:DOI: 10.1016/0378-3758(95)00162-X
[BibTeX] [Abstract] Lattice Path Combinatorics and Applications [PDF]
The self-avoiding walk, restricted to a strip, is considered in the context of linguistic combinatorics.

@article{Zeilberger1996a,
Author = {Zeilberger, Doron},
Date-Modified = {2013-03-05 09:44:22 +0000},
Doi = {DOI: 10.1016/0378-3758(95)00162-X},
Issn = {0378-3758},
Journal = {Journal of Statistical Planning and Inference},
Keywords = {The Sch{\"u}tzenberger methodology},
Note = {Lattice Path Combinatorics and Applications},
Number = {1},
Pages = {135 - 138},
Title = {Self-avoiding walks, the language of science, and Fibonacci numbers},
Url = {http://www.sciencedirect.com/science/article/B6V0M-3VVCJ90-C/2/668ed790f084aba978cb5ef770f5e92c},
Volume = {54},
Year = {1996},
Abstract = {
The self-avoiding walk, restricted to a strip, is considered in the context of linguistic combinatorics.},
Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V0M-3VVCJ90-C/2/668ed790f084aba978cb5ef770f5e92c},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/0378-3758(95)00162-X}}

• J. Noonan and D. Zeilberger. — The enumeration of permutations with a prescribed number of “forbidden” patterns. — Advances in applied mathematics, 17.4:381-407, 1996.
[BibTeX]
@article{NoonanZeilberger1996,
Author = {Noonan, J. and Zeilberger, D.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Advances in Applied Mathematics},
Number = {4},
Pages = {381-407},
Title = {The enumeration of permutations with a prescribed number of forbidden'' patterns},
Volume = {17},
Year = {1996}}

• R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane. — Algebraic description of coordination sequences and exact topological densities for zeolites. — Acta crystallographica section a: foundations of crystallography, 52.6:879-889, 1996.
[BibTeX]
@article{Grosse-KunstleveBrunnerSloane1996,
Author = {Grosse-Kunstleve, R. W. and Brunner, G. O. and Sloane, N. J. A.},
Date-Modified = {2013-03-05 09:07:30 +0000},
Journal = {Acta Crystallographica Section A: Foundations of Crystallography},
Number = {6},
Pages = {879-889},
Title = {Algebraic description of coordination sequences and exact topological densities for zeolites},
Volume = {52},
Year = {1996}}

### 1995

• Peter Paule and Markus Schorn. — A Mathematica version of Zeilberger’s algorithm for proving binomial coefficient identities. — 20.5/6:673-698, 1995.
[BibTeX]
@article{PauleSchorn1995,
Author = {Paule, Peter and Schorn, Markus},
Date-Modified = {2013-03-05 09:45:39 +0000},
Journal = jsc,
Number = {5/6},
Owner = {bs},
Pages = {673--698},
Title = {A {M}athematica Version of {Z}eilberger's Algorithm for Proving Binomial Coefficient Identities},
Volume = 20,
Year = 1995,
Bdsk-File-1 = {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}}

• István Nemes and Marko Petkovšek. — \tt RComp: a \sl Mathematica\/ package for computing with recursive sequences. — Jsc, 20.5/6:745-753, 1995.
[BibTeX]
@article{NemesPetkovsek1995,
Author = {Nemes, Istv{\'a}n and Petkov{\v s}ek, Marko},
Date-Modified = {2013-03-05 09:45:19 +0000},
Journal = jsc,
Number = {5/6},
Owner = {bs},
Pages = {745--753},
Title = {{\tt RComp}: A {\sl Mathematica\/} Package for Computing with Recursive Sequences},
Volume = 20,
Year = 1995,
Bdsk-File-1 = {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}}

• Philippe Flajolet and Bruno Salvy. — Computer algebra libraries for combinatorial structures. — Jsc, 20.5-6:653-671, 1995.
doi:10.1006/jsco.1995.1070
[BibTeX] [Abstract]
This paper introduces the framework of decomposable combinatorial structures and their traversal algorithms. A combinatorial type is decomposable if it admits a specification in terms of unions, products, sequences, sets, and cycles, either in the labelled or in the unlabelled context. Many properties of decomposable structures are decidable. Generating function equations, counting sequences, and random generation algorithms can be compiled from specifications. Asymptotic properties can be determined automatically for a reasonably large subclass. Maple libraries that implement such decision procedures are briefly surveyed (LUO, combstruct, equivalent). In addition, libraries for manipulating holonomic sequences and functions are presented (gfun, Mgfun).

@article{FlajoletSalvy1995,
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Modified = {2013-03-05 09:45:05 +0000},
Doi = {10.1006/jsco.1995.1070},
Journal = jsc,
Number = {5-6},
Pages = {653--671},
Title = {Computer Algebra Libraries for Combinatorial Structures},
Volume = 20,
Year = 1995,
Abstract = {This paper introduces the framework of decomposable combinatorial structures and their traversal algorithms. A combinatorial type is decomposable if it admits a specification in terms of unions, products, sequences, sets, and cycles, either in the labelled or in the unlabelled context. Many properties of decomposable structures are decidable. Generating function equations, counting sequences, and random generation algorithms can be compiled from specifications. Asymptotic properties can be determined automatically for a reasonably large subclass. Maple libraries that implement such decision procedures are briefly surveyed (LUO, combstruct, equivalent). In addition, libraries for manipulating holonomic sequences and functions are presented (gfun, Mgfun).},
Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1995.1070}}

• François Bergeron and Ulrike Sattler. — Constructible differentially finite algebraic series in several variables. — Theoretical computer science, 144.1-2:59-65, 1995.
[BibTeX]
@article{BergeronSattler1995,
Author = {Bergeron, Fran{\c c}ois and Sattler, Ulrike},
Date-Modified = {2013-03-05 09:44:48 +0000},
Journal = {Theoretical Computer Science},
Month = jun,
Number = {1-2},
Pages = {59--65},
Title = {Constructible differentially finite algebraic series in several variables},
Volume = {144},
Year = {1995},
Bdsk-File-1 = {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}}

### 1994

• Volker Strehl. — Binomial identities — combinatorial and algorithmic aspects. — Discrete mathematics, 136.1-3:309-346, 1994.
doi:DOI: 10.1016/0012-365X(94)00118-3
[BibTeX] [Abstract] [PDF]
The problem of proving a particular binomial identity is taken as an opportunity to discuss various aspects of this field and to discuss various proof techniques in an exemplary way. In particular, the unifying role of the hypergeometric nature of binomial identities is underlined. This aspect is also basic for combinatorial models and techniques, developed during the last decade, and for the recent algorithmic proof procedures. “Much of mathematics comes from looking at very simple examples from a more general perspective. Hypergeometric functions are a good example of this.”

@article{Strehl1994,
Author = {Strehl, Volker},
Date-Modified = {2013-03-05 09:45:55 +0000},
Doi = {DOI: 10.1016/0012-365X(94)00118-3},
Issn = {0012-365X},
Journal = {Discrete Mathematics},
Number = {1-3},
Pages = {309--346},
Title = {Binomial identities -- combinatorial and algorithmic aspects},
Url = {http://www.sciencedirect.com/science/article/B6V00-45F5RBY-1B/2/187ce6b44b86c2c73180ba5f37b08878},
Volume = {136},
Year = {1994},
Abstract = {
The problem of proving a particular binomial identity is taken as an opportunity to discuss various aspects of this field and to discuss various proof techniques in an exemplary way. In particular, the unifying role of the hypergeometric nature of binomial identities is underlined. This aspect is also basic for combinatorial models and techniques, developed during the last decade, and for the recent algorithmic proof procedures.
Much of mathematics comes from looking at very simple examples from a more general perspective. Hypergeometric functions are a good example of this.''},
Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V00-45F5RBY-1B/2/187ce6b44b86c2c73180ba5f37b08878},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/0012-365X(94)00118-3}}

### 1993

• Marko Petkovšek and Bruno Salvy. — Finding all hypergeometric solutions of linear differential equations. — Issac’93, Ed. Manuel Bronstein. New York: ACM Press, pages 27-33, 1993.
doi:10.1145/164081.164087
[BibTeX] [Abstract]
Hypergeometric sequences are such that the quotient of two successive terms is a fixed rational function of the index. We give a generalization of M.~Petkovšek’s algorithm to find all hypergeometric sequence solutions of linear recurrences, and we describe a program to find all hypergeometric functions that solve a linear differential equation.

@inproceedings{PetkovsekSalvy1993,
Author = {Petkov{\v s}ek, Marko and Salvy, Bruno},
Booktitle = {ISSAC'93},
Date-Modified = {2013-03-05 09:46:10 +0000},
Doi = {10.1145/164081.164087},
Editor = {Bronstein, Manuel},
Month = jul,
Pages = {27--33},
Publisher = {ACM Press},
Title = {Finding all hypergeometric solutions of linear differential equations},
Year = 1993,
Abstract = {Hypergeometric sequences are such that the quotient of two
successive terms is a fixed rational function of the index. We give a
generalization of
M.~Petkov{\v s}ek's algorithm to find all hypergeometric sequence
solutions of linear recurrences, and we
describe a program to find all hypergeometric functions that solve a linear
differential equation.},
Bdsk-Url-1 = {http://dx.doi.org/10.1145/164081.164087}}

### 1992

• F. Bergeron and S. Plouffe. — Computing the generating function of a series given its first terms. — 1.4:308-312, 1992.
[BibTeX]
@article{BergeronPlouffe1992,
Author = {Bergeron, F. and Plouffe, S.},
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