Matthieu Rosenfeld

Research

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 ℤ2 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:

  1. Avoiding two consecutive blocks of same size and same sum over ℤ2, with Michaël Rao. (arXiv)

In Journals:

  1. 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:

  1. Every binary pattern of length greater than 14 is abelian-2-avoidable.
    Mathematical Foundations of Computer Science, 2016 (html).
  2. Avoidability of formulas with two variables, with Pascal Ochem.
    Developments in Language Theory, 2016 (arxiv).

Other Talks and Seminars

  1. Avoiding repetitions in words, One Day Meeting in Discrete Structures 2
    LIP, April 2016
  2. Every long enough binary pattern is abelian 2-avoidable, Séminaire AlGCo
    LIRMM, February 2016
  3. Avoidability of long abelian-squares, SeqBio, 2015
  4. Décider si un mot morphic évite les puissances abeliennes, Séminaires de l'équipe Combinatoire & Algorithmes
    LITIS, November 2015