The finite index basis property
Discrete Mathematics
2015-02-23 v7 Combinatorics
Abstract
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, namemly the class of tree sets. We prove as a main result that for a uniformly recurrent tree set , a finite bifix code on the alphabet is -maximal of -degree if and only if it is the basis of a subgroup of index of the free group on .
Cite
@article{arxiv.1305.0127,
title = {The finite index basis property},
author = {Valérie Berthé and Clelia De Felice and Francesco Dolce and Julien Leroy and Dominique Perrin and Christophe Reutenauer and Giuseppina Rindone},
journal= {arXiv preprint arXiv:1305.0127},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1011.5369, arXiv:1305.0120