Publications

Most of my papers are available in electronic form from the list below.

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Usually, I put preliminary versions on arXiv. You can be informed of new ones by subscribing to this rss feed.

2017

  • Y. Bugeaud, A. Dujella, T. Pejkovic, and B. Salvy, “Absolute real root separation,” American Mathematical Monthly, 2017.
    arXiv BibTeX Abstract
  • A. Bostan, P. Lairez, and B. Salvy, “Multiple binomial sums,” Journal of Symbolic Computation, vol. 80, pp. 351–386, 2017.
    arXiv doi BibTeX Abstract
  • A. Bostan, L. Dumont, and B. Salvy, “Algebraic Diagonals and Walks: Algorithms, Bounds, Complexity,” Journal of Symbolic Computation, vol. 83, pp. 68–92, 2017.
    arXiv doi BibTeX Abstract
    This is an extended version of the ISSAC’15 article, with more precise results and more detailed proofs.

2016

  • R. Serra, D. Arzelier, M. Joldes, J.-B. Lasserre, A. Rondepierre, and B. Salvy, “Fast and accurate computation of orbital collision probability for short-term encounters,” Journal of Guidance, Control, and Dynamics, vol. 39, no. 5, pp. 1009–1021, 2016.
    PDF doi BibTeX Abstract
  • S. Melczer and B. Salvy, “Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables,” in ISSAC’16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, 2016, pp. 333–340.
    PDF from ACM doi BibTeX Abstract
  • A. Bostan, L. Dumont, and B. Salvy, “Efficient Algorithms for Mixed Creative Telescoping,” in ISSAC’16—Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation, 2016, pp. 127–134.
    PDF from ACM doi BibTeX Abstract

2015

  • S. Maulat and B. Salvy, “Formulas for Continued Fractions: An Automated Guess and Prove Approach,” in ISSAC’15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, 2015, pp. 275–282.
    arXiv PDF from ACM doi BibTeX Abstract
    See accompanying Maple worksheet on arXiv.
  • A. Bostan, L. Dumont, and B. Salvy, “Algebraic Diagonals and Walks,” in ISSAC’15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, 2015, pp. 77–84.
    PDF from ACM doi BibTeX Abstract
  • M. Bardet, J.-C. Faugère, and B. Salvy, “On the Complexity of the F5 Gröbner basis Algorithm,” Journal of Symbolic Computation, vol. 70, pp. 49–70, 2015.
    arXiv doi BibTeX Abstract

2014

  • R. Serra, D. Arzelier, M. Joldes, J.-B. Lasserre, A. Rondepierre, and B. Salvy, “A New Method to Compute the Probability of Collision for Short-term Space Encounters,” in AIAA/AAS Astrodynamics Specialist Conference, 2014, pp. 1–7.
    doi BibTeX Abstract
  • A. Bostan, K. Raschel, and B. Salvy, “Non-D-finite excursions in the quarter plane,” Journal of Combinatorial Theory, Series A, vol. 121, pp. 45–63, 2014.
    arXiv doi BibTeX Abstract

2013

  • B. Salvy, “Asymptotics of linear divide-and-conquer recurrences.” Summary of Philippe Dumas’ talk at the Flajolet seminar, IHP., pp. 1–8, 2013.
    PDF BibTeX
  • B. Salvy, “Philippe Flajolet and Symbolic Computation.” Preprint. To appear in Philippe Flajolet’s collected works., 2013.
    PDF BibTeX
  • A. Bostan, P. Lairez, and B. Salvy, “Creative telescoping for rational functions using the Griffiths-Dwork method,” in ISSAC ’13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013, pp. 93–100.
    PDF from ACM doi BibTeX Abstract
  • M. Bardet, J.-C. Faugère, B. Salvy, and P.-J. Spaenlehauer, “On the Complexity of Solving Quadratic Boolean Systems,” Journal of Complexity, vol. 29, no. 1, pp. 53–75, 2013.
    arXiv doi BibTeX Abstract

2012

  • C. Pivoteau, B. Salvy, and M. Soria, “Algorithms for Combinatorial Structures: Well-founded systems and Newton iterations,” Journal of Combinatorial Theory, Series A, vol. 119, pp. 1711–1773, 2012.
    arXiv doi BibTeX Abstract
  • A. Bostan, F. Chyzak, Z. Li, and B. Salvy, “Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators,” in ISSAC ’12: Proceedings of the twenty-fifth International Symposium on Symbolic and Algebraic Computation, 2012, pp. 99–106.
    PDF from ACM doi BibTeX Abstract
  • A. Bostan, M. F. I. Chowdhury, R. Lebreton, B. Salvy, and É. Schost, “Power Series Solutions of Singular (q)-Differential Equations,” in ISSAC ’12: Proceedings of the twenty-fifth International Symposium on Symbolic and Algebraic Computation, 2012, pp. 107–114.
    PDF from ACM doi BibTeX Abstract

2011

  • J.-G. Dumas, L. Fousse, and B. Salvy, “Simultaneous modular reduction and Kronecker substitution for small finite fields,” Journal of Symbolic Computation, vol. 46, no. 7, pp. 823–840, 2011.
    doi BibTeX Abstract
  • F. Chyzak, J. H. Davenport, C. Koutschan, and B. Salvy, “On Kahan’s Rules for Determining Branch Cuts,” in Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2011), 2011, pp. 47–51.
    arXiv doi BibTeX Abstract

2010

  • B. Salvy and J. Shackell, “Measured limits and multiseries,” Journal of the London Mathematical Society, vol. 82, no. 3, pp. 747–762, 2010.
    PDF doi BibTeX Abstract
  • M. Mezzarobba and B. Salvy, “Effective Bounds for P-Recursive Sequences,” Journal of Symbolic Computation, vol. 45, no. 10, pp. 1075–1096, Oct. 2010.
    arXiv doi BibTeX Abstract
  • P. Flajolet, S. Gerhold, and B. Salvy, “Lindelöf Representations and (Non-)Holonomic Sequences,” The Electronic Journal of Combinatorics, vol. 17, no. 1, pp. 1–28, 2010.
    arXiv PDF BibTeX Abstract
  • A. Bostan, B. Salvy, and K. Tran, “Generating functions of Chebyshev-like polynomials,” International Journal of Number Theory, vol. 6, no. 7, pp. 1659–1667, 2010.
    arXiv doi BibTeX Abstract
  • A. Bostan, B. Salvy, and É. Schost, “Fast conversion algorithms for orthogonal polynomials,” Linear Algebra and its Applications, vol. 432, no. 1, pp. 249–258, Jan. 2010.
    arXiv doi BibTeX Abstract
  • A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, and B. Salvy, “The Dynamic Dictionary of Mathematical Functions (DDMF),” in The Third International Congress on Mathematical Software (ICMS 2010), 2010, vol. 6327, pp. 35–41.
    doi BibTeX Abstract

2009

  • P. Clote, E. Kranakis, D. Krizanc, and B. Salvy, “Asymptotics of Canonical and Saturated RNA Secondary Structures,” Journal of Bioinformatics and Computational Biology, vol. 7, no. 5, pp. 869–893, Oct. 2009.
    PDF doi BibTeX Abstract
  • F. Chyzak, M. Kauers, and B. Salvy, “A Non-Holonomic Systems Approach to Special Function Identities,” in ISSAC ’09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation, 2009, pp. 111–118.
    PDF from ACM doi BibTeX Abstract
  • A. Benoit and B. Salvy, “Chebyshev Expansions for Solutions of Linear Differential Equations,” in ISSAC ’09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation, 2009, pp. 23–30.
    PDF from ACM doi BibTeX Abstract

2008

  • C. Pivoteau, B. Salvy, and M. Soria, “Boltzmann Oracle for Combinatorial Systems,” in Algorithms, Trees, Combinatorics and Probabilities, 2008, pp. 475–488.
    PDF BibTeX Abstract
  • C. Gomez and B. Salvy, “Calcul Formel,” Les Techniques de l’Ingénieur, vol. Dossier AF1460, pp. 1–20, 2008.
    BibTeX
  • J.-G. Dumas, L. Fousse, and B. Salvy, “Compressed Modular Matrix Multiplication,” in Milestones in Computer Algebra (MICA 2008), 2008.
    arXiv BibTeX Abstract
  • A. Bostan, B. Salvy, and É. Schost, “Power Series Composition and Change of Basis,” in ISSAC’08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, 2008, pp. 269–276.
    PDF from ACM doi BibTeX Abstract
  • A. Bostan, F. Morain, B. Salvy, and É. Schost, “Fast algorithms for computing isogenies between elliptic curves,” Mathematics of Computation, vol. 77, no. 263, pp. 1755–1778, 2008.
    arXiv doi BibTeX Abstract
  • J. M. Borwein and B. Salvy, “A proof of a recursion for Bessel moments,” Experimental Mathematics, vol. 17, no. 2, pp. 223–230, 2008.
    PDF doi BibTeX Abstract

2007

  • M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn, “On Location and Approximation of Clusters of Zeroes: Case of Embedding Dimension One,” Foundations of Computational Mathematics, vol. 7, no. 1, pp. 1–58, 2007.
    doi BibTeX Abstract
  • A. Bostan, F. Chyzak, F. Ollivier, B. Salvy, É. Schost, and A. Sedoglavic, “Fast computation of power series solutions of systems of differential equations,” in SODA’07, 2007, pp. 1012–1021.
    arXiv BibTeX Abstract
  • A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, and É. Schost, “Differential equations for algebraic functions,” in ISSAC’07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007, pp. 25–32.
    PDF from ACM doi BibTeX Abstract

2006

  • A. Bostan, P. Flajolet, B. Salvy, and É. Schost, “Fast Computation of Special Resultants,” Journal of Symbolic Computation, vol. 41, no. 1, pp. 1–29, Jan. 2006.
    doi BibTeX Abstract
  • A. Bostan, F. Chyzak, T. Cluzeau, and B. Salvy, “Low Complexity Algorithms for Linear Recurrences,” in ISSAC’06, 2006, pp. 31–38.
    PDF from ACM doi BibTeX Abstract

2005

  • B. Salvy, “D-Finiteness: Algorithms and Applications,” in ISSAC’05, 2005, pp. 2–3.
    PDF from ACM doi BibTeX
    Abstract for an invited talk. Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, Beijing, July 2005.
  • M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn, “On Location and Approximation of Clusters of Zeroes of Analytic Functions,” Foundations of Computational Mathematics, vol. 5, no. 3, pp. 257–311, 2005.
    doi BibTeX Abstract
  • P. Flajolet, S. Gerhold, and B. Salvy, “On the non-holonomic character of logarithms, powers, and the nth prime function,” The Electronic Journal of Combinatorics, vol. 11, no. 2, 2005.
    PDF BibTeX Abstract
  • F. Chyzak, M. Mishna, and B. Salvy, “Effective Scalar Products of D-finite Symmetric Functions,” Journal of Combinatorial Theory. Series A, vol. 112, no. 1, pp. 1–43, Oct. 2005.
    arXiv doi BibTeX Abstract
  • A. Bostan, T. Cluzeau, and B. Salvy, “Fast Algorithms for Polynomial Solutions of Linear Differential Equations,” in ISSAC’05, New York, 2005, pp. 45–52.
    PDF from ACM doi BibTeX Abstract
    Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, July 2005, Beijing, China.
  • M. Bardet, J.-C. Faugère, B. Salvy, and B.-Y. Yang, “Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems,” in MEGA’05, 2005.
    BibTeX Abstract

2004

  • P. Flajolet, B. Salvy, and G. Schaeffer, “Airy Phenomena and Analytic Combinatorics of Connected Graphs,” The Electronic Journal of Combinatorics, vol. 11, no. 1, p. R34, 2004.
    PDF BibTeX Abstract
  • A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt, “Complexity Issues in Bivariate Polynomial Factorization,” in Symbolic and Algebraic Computation, 2004, pp. 42–49.
    PDF from ACM doi BibTeX Abstract
    Proceedings of ISSAC’04, Santander, July 2004
  • M. Bardet, J.-C. Faugère, and B. Salvy, “On the Complexity of Gröbner basis computation of Semi-regular Overdetermined algebraic equations,” in International Conference on Polynomial System Solving, 2004, pp. 71–74.
    BibTeX Abstract

2003

  • L. Meunier and B. Salvy, “ESF: An Automatically Generated Encyclopedia of Special Functions,” in Symbolic and Algebraic Computation, 2003, pp. 199–205.
    PDF from ACM doi BibTeX Abstract
    Proceedings of ISSAC’03, Philadelphia, August 2003.
  • A. Bostan, B. Salvy, and É. Schost, “Fast Algorithms for Zero-Dimensional Polynomial Systems Using Duality,” Applicable Algebra in Engineering, Communication and Computing, vol. 14, no. 4, pp. 239–272, 2003.
    doi BibTeX Abstract

2002

  • P. Nicodème, B. Salvy, and P. Flajolet, “Motif Statistics,” Theoretical Computer Science, vol. 287, no. 2, pp. 593–618, 2002.
    doi BibTeX Abstract
  • R. Cori, D. Rossin, and B. Salvy, “Polynomial Ideals for Sandpiles and their Gröbner Bases,” Theoretical Computer Science, vol. 276, no. 1, pp. 1–15, 2002.
    doi BibTeX Abstract
  • F. Chyzak, M. Mishna, and B. Salvy, “Effective D-finite Symmetric Functions,” in 14th Conference of Formal Power Series and Algebraic Combinatorics, Melbourne, Australia, 2002, pp. 19.1–19.12.
    BibTeX

2001

  • B. Salvy, “Even-Odd Set Partitions, Saddle-Point Method and Wyman Admissibility,” Institut National de Recherche en Informatique et en Automatique, Research Report 4201, 2001.
    BibTeX
  • L. Meunier and B. Salvy, “Automatically Generated Encyclopedia of Special Functions,” in Mathematical Knowledge Management, 2001.
    PDF BibTeX Abstract
  • M. Giusti, G. Lecerf, and B. Salvy, “A Gröbner Free Alternative for Polynomial System Solving,” Journal of Complexity, vol. 17, no. 1, pp. 154–211, Mar. 2001.
    doi BibTeX Abstract

2000

  • M. Giusti, K. Hägele, G. Lecerf, J. Marchand, and B. Salvy, “Computing the Dimension of a Projective Variety: the Projective Noether Maple Package,” Journal of Symbolic Computation, vol. 30, no. 3, pp. 291–307, Sep. 2000.
    doi BibTeX Abstract

1999

  • B. Salvy and J. Shackell, “Symbolic Asymptotics: Multiseries of Inverse Functions,” Journal of Symbolic Computation, vol. 27, no. 6, pp. 543–563, 1999.
    doi BibTeX Abstract
  • P. Nicodème, B. Salvy, and P. Flajolet, “Motif Statistics,” in Algorithms – ESA’99, 1999, no. 1643, pp. 194–211.
    PDF doi BibTeX Abstract

1998

  • B. Salvy and J. Shackell, “Symbolic Asymptotics: Functions of Two Variables, Implicit Functions,” Journal of Symbolic Computation, vol. 25, no. 3, pp. 329–349, Mar. 1998.
    doi BibTeX Abstract
  • P. Flajolet and B. Salvy, “Euler Sums and Contour Integral Representations,” Experimental Mathematics, vol. 7, no. 1, pp. 15–35, 1998.
    PDF BibTeX Abstract
  • F. Chyzak and B. Salvy, “Non-commutative Elimination in Ore Algebras Proves Multivariate Holonomic Identities,” Journal of Symbolic Computation, vol. 26, no. 2, pp. 187–227, 1998.
    doi BibTeX Abstract

1997

  • L. Habsieger and B. Salvy, “On Integer Chebyshev Polynomials,” Mathematics of Computation, vol. 66, no. 218, pp. 763–770, 1997.
    PDF doi BibTeX Abstract
  • P. Flajolet and B. Salvy, “The SIGSAM Challenges: Symbolic Asymptotics in Practice,” SIGSAM Bulletin, vol. 31, no. 4, pp. 36–47, Dec. 1997.
    PDF from ACM doi BibTeX Abstract

1996

  • D. Richardson, B. Salvy, J. Shackell, and J. Van der Hoeven, “Asymptotic Expansions of exp-log Functions,” in Symbolic and Algebraic Computation, New York, 1996, pp. 309–313.
    PDF from ACM doi BibTeX Abstract
    Proceedings ISSAC’96, Zürich, July 1996
  • X. Gourdon and B. Salvy, “Effective asymptotics of linear recurrences with rational coefficients,” Discrete Mathematics, vol. 153, no. 1–3, pp. 145–163, 1996.
    doi BibTeX Abstract

1995

  • J. Shackell and B. Salvy, “Asymptotic Forms and Algebraic Differential Equations,” Journal of Symbolic Computation, vol. 20, no. 2, pp. 169–177, 1995.
    doi BibTeX Abstract
  • B. Salvy and S. Y. Slavyanov, “A Combinatorial Problem in the Classification of Second-Order Linear ODE’s,” Institut National de Recherche en Informatique et en Automatique, Research Report 2600, 1995.
    BibTeX
  • S. P. Lipshitz, T. C. Scott, and B. Salvy, “On the Acoustic Impedance of Baffled Strip Radiators,” Journal of the Audio Engineering Society, vol. 43, no. 7/8, pp. 573–580, Jul. 1995.
    BibTeX Abstract
  • C. Gomez, B. Salvy, and P. Zimmermann, Calcul formel : mode d’emploi. Exemples en Maple. Masson, 1995.
    BibTeX
  • P. Flajolet and B. Salvy, “Computer Algebra Libraries for Combinatorial Structures,” Journal of Symbolic Computation, vol. 20, no. 5-6, pp. 653–671, 1995.
    doi BibTeX Abstract
  • P. Flajolet, G. Labelle, L. Laforest, and B. Salvy, “Hypergeometrics and the cost structure of quadtrees,” Random Structures & Algorithms, vol. 7, no. 2, pp. 117–144, 1995.
    doi BibTeX Abstract
  • P. Dumas and B. Salvy, “Maple and the Putnam Competition,” The Maple Technical Newsletter, vol. 2, no. 2, pp. 63–68, 1995.
    BibTeX

1994

  • B. Salvy and P. Zimmermann, “Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable,” toms, vol. 20, no. 2, pp. 163–177, 1994.
    PDF from ACM doi BibTeX Abstract
  • B. Salvy, “Fast Computation of Some Asymptotic Functional Inverses,” Journal of Symbolic Computation, vol. 17, no. 3, pp. 227–236, 1994.
    doi BibTeX Abstract

1993

  • B. Salvy, “Efficient programming in Maple: a case study,” SIGSAM Bulletin, vol. 27, no. 2, pp. 1–12, Apr. 1993.
    PDF from ACM doi BibTeX Abstract
  • M. Petkovšek and B. Salvy, “Finding all hypergeometric solutions of linear differential equations,” in ISSAC’93, New York, 1993, pp. 27–33.
    PDF from ACM doi BibTeX Abstract
  • X. Gourdon and B. Salvy, “Computing one million digits of \sqrt2,” The Maple Technical Newsletter, vol. 10, pp. 66–71, 1993.
    BibTeX Abstract
  • X. Gourdon and B. Salvy, “Asymptotics of linear recurrences with rational coefficients,” in Formal Power Series and Algebraic Combinatorics, 1993, pp. 253–266.
    BibTeX Abstract
  • P. Flajolet and B. Salvy, “A Finite Sum of Products of Binomial Coefficients,” SIAM Review, vol. 35, no. 4, pp. 645–646, 1993.
    PDF doi BibTeX
  • P. Flajolet, X. Gourdon, and B. Salvy, “Sur une famille de polynômes issus de l’analyse numérique,” Gazette des Mathématiciens, vol. 55, pp. 67–78, Jan. 1993.
    BibTeX
  • M. Bronstein and B. Salvy, “Full Partial Fraction Decomposition of Rational Functions,” in ISSAC’93, New York, 1993, pp. 157–160.
    PDF from ACM doi BibTeX Abstract

1992

  • B. Salvy and J. Shackell, “Asymptotic expansions of functional inverses,” in Symbolic and Algebraic Computation, New York, 1992, pp. 130–137.
    PDF from ACM doi BibTeX Abstract
    Proceedings of ISSAC’92, Berkeley, July 1992.
  • B. Salvy, “General Asymptotic Scales and Computer Algebra,” in Asymptotic and Numerical Methods for Partial Differential Equations, Critical Parameters and Domain Decomposition, 1992.
    BibTeX Abstract
  • F. Bergeron, P. Flajolet, and B. Salvy, “Varieties of Increasing Trees,” in CAAP’92, 1992, vol. 581, pp. 24–48.
    doi BibTeX Abstract

1991

  • B. Salvy, “Three ways to get Stirling’s formula in Maple,” The Maple Technical Newsletter, vol. 5, pp. 32–42, 1991.
    BibTeX
  • B. Salvy, “Asymptotique automatique et fonctions génératrices,” Thèse de Doctorat, École polytechnique, 1991.
    BibTeX
  • B. Salvy, “Examples of automatic asymptotic expansions,” SIGSAM Bulletin, vol. 25, no. 2, pp. 4–17, Apr. 1991.
    PDF from ACM doi BibTeX Abstract
  • P. Flajolet, B. Salvy, and P. Zimmermann, “Automatic Average-case Analysis of Algorithms,” Theoretical Computer Science, vol. 79, no. 1, pp. 37–109, 1991.
    doi BibTeX Abstract

1989

  • P. Flajolet, B. Salvy, and P. Zimmermann, “Lambda-Upsilon-Omega: The 1989 CookBook,” Institut National de Recherche en Informatique et en Automatique, Research Report 1073, 1989.
    BibTeX
  • P. Flajolet, B. Salvy, and P. Zimmermann, “Lambda-Upsilon-Omega: An Assistant Algorithms Analyzer,” in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 1989, vol. 357, pp. 201–212.
    doi BibTeX Abstract

1988

  • B. Salvy, “Fonctions génératrices et asymptotique automatique,” Université Paris XI, Rapport de DEA, 1988.
    BibTeX

1987

  • B. Salvy, “Calcul automatique du développement asymptotique lorsque leur rang tend vers l’infini des coefficients des développements en série de Laurent de certaines fonctions génératrices,” École polytechnique, Rapport d’option, 1987.
    BibTeX