[en] 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
Disciplines :
Mathématiques
Auteur, co-auteur :
Berthé, V.
De Felice, C.
Dolce, F.
LEROY, Julien ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
