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   The finite index basis property; ; et al 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 ▲] Detailed reference viewed: 102 (4 UL)Return words in tree setsLeroy, Julien  Scientific Conference (2014, September) Detailed reference viewed: 34 (1 UL)Return words in tree setsLeroy, Julien Presentation (2014, July) Detailed reference viewed: 33 (1 UL)S-adic characterization of sequence with complexity 2nLeroy, Julien Presentation (2014, April) Detailed reference viewed: 45 (1 UL)Factor complexity of S-adic sequencesLeroy, Julien Presentation (2014, January) Detailed reference viewed: 47 (1 UL)Different frameworks for cobham's theorem in RLeroy, Julien Scientific Conference (2014, January) Detailed reference viewed: 47 (1 UL)Acyclic, connected and tree sets; ; et al in Monatshefte für Mathematik (2014) Detailed reference viewed: 125 (2 UL) An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n + 1) - p(n) ≤ 2Leroy, Julien 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 ▲] Detailed reference viewed: 51 (4 UL)An analogue of Cobham's theorem for graph directed iterated function systems; Leroy, Julien ; in Advances in Mathematics (2014) Detailed reference viewed: 107 (3 UL)Bifix codes and interval exchanges; ; et al in Journal of Pure and Applied Algebra (2014) Detailed reference viewed: 118 (3 UL)An analogue of Cobham's theorem for graph directed iterated function systemsLeroy, Julien Presentation (2013, December) Detailed reference viewed: 36 (1 UL)A bridge between graph directed iterated function systems and Büchi automataLeroy, Julien Scientific Conference (2013, November) Detailed reference viewed: 43 (1 UL)Factor complexity of S-adic sequencesLeroy, Julien Presentation (2013, September) Detailed reference viewed: 36 (1 UL)Factor complexity of S-adic sequencesLeroy, Julien Scientific Conference (2013, June) Detailed reference viewed: 40 (2 UL)Cobham's theorem for abstract numeration systems; Leroy, Julien ; E-print/Working paper (2013) Detailed reference viewed: 54 (1 UL)Do the properties of an $S$-adic representation determine factor complexity?; Leroy, Julien ; in Journal of Integer Sequences (2013), 16(2), 132630 Detailed reference viewed: 36 (1 UL)A combinatorial proof of $S$-adicity for sequences with linear complexityLeroy, Julien ; in Integers (2013), 13 Detailed reference viewed: 116 (2 UL)An S-adic characterization of minimal subshifts with first difference of complexity 1 <=p(n+1)-p(n)<=2Leroy, Julien E-print/Working paper (2013) Detailed reference viewed: 67 (1 UL)S-adic representations using Rauzy graphsLeroy, Julien Scientific Conference (2012, July) Detailed reference viewed: 49 (1 UL)
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