The finite index basis property

in Journal of Pure and Applied Algebra (2015)

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems ... [more ▼]

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of tree sets. We prove as a main result that for a uniformly recurrent tree set S, a finite bifix code X on the alphabet A is S-maximal of S-degree d if and only if it is the basis of a subgroup of index d of the free group on A [less ▲]

Return words in tree sets

Presentation (2014, July)

Different frameworks for cobham's theorem in R

Scientific Conference (2014, January)

An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n + 1) - p(n) ≤ 2

in Discrete Mathematics and Theoretical Computer Science (2014), 16(1), 233--286

In [Ergodic Theory Dynam. System, 16 (1996) 663–682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S)≤ 3^27. In this paper, we improve ... [more ▼]

In [Ergodic Theory Dynam. System, 16 (1996) 663–682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S)≤ 3^27. In this paper, we improve this result by giving an S-adic charaterization of these subshifts with a set S of 5 morphisms, solving by this way the S-adic conjecture for this particular case. [less ▲]

An analogue of Cobham's theorem for graph directed iterated function systems

in Advances in Mathematics (2014)

Bifix codes and interval exchanges

in Journal of Pure and Applied Algebra (2014)

A bridge between graph directed iterated function systems and Büchi automata

Scientific Conference (2013, November)

Factor complexity of S-adic sequences

Scientific Conference (2013, June)

An S-adic characterization of minimal subshifts with first difference of complexity 1 <=p(n+1)-p(n)<=2

E-print/Working paper (2013)

Do the properties of an $S$-adic representation determine factor complexity?

in Journal of Integer Sequences (2013), 16(2), 132630