The topic of my PhD is the avoidability of substructures in words. In particular, I studied the avoidability of patterns and powers in the usual, the abelian or the additive sens.
One example of such a result is: There exists an infinite word over a finite subset of ℤ^{2} that does not contain two consecutive factors of same size and same sum. It is still open whether it is also possible over a finite subset of ℤ or not (Note that Szemerédi's theorem implies that it is not possible without the "same size" condition).
Publications
In preparation:
- Avoiding two consecutive blocks of same size and same sum over ℤ^{2},
with Michaël Rao. (arXiv)
In Journals:
- Avoidability of long k-abelian repetitions,
with Michaël Rao.
In Mathematics of Computation. (html) (arXiv)
A preliminary version was presented in: Mons Theoretical Computer Science Days 2014.
In Conferences:
- Every binary pattern of length greater than 14 is abelian-2-avoidable.
Mathematical Foundations of Computer Science, 2016 (html). - Avoidability of formulas with two variables,
with Pascal Ochem.
Developments in Language Theory, 2016 (arxiv).
Other Talks and Seminars
- Avoiding repetitions in words, One Day Meeting in Discrete Structures 2
LIP, April 2016 - Every long enough binary pattern is abelian 2-avoidable, Séminaire AlGCo
LIRMM, February 2016 - Avoidability of long abelian-squares, SeqBio, 2015
- Décider si un mot morphic évite les puissances abeliennes,
Séminaires de l'équipe Combinatoire & Algorithmes
LITIS, November 2015