Reference : The finite index basis property
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
The finite index basis property
Berthé, V. [> >]
De Felice, C. [> >]
Dolce, F. [> >]
Leroy, Julien [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Perrin, D. [> >]
Reutenauer, C. [> >]
Rindone, G. [> >]
Journal of Pure and Applied Algebra
Elsevier Science
Yes (verified by ORBilu)
[en] Computer Science - Discrete Mathematics ; Mathematics - Combinatorics
[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

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