Acyclic, connected and tree sets
Combinatorics
2015-02-24 v6 Formal Languages and Automata Theory
Abstract
Given a set of words, one associates to each word in an undirected graph, called its extension graph, and which describes the possible extensions of on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected or a tree. We prove that in a uniformly recurrent tree set, the sets of first return words are bases of the free group on the alphabet. Concerning acyclic sets, we prove as a main result that a set is acyclic if and only if any bifix code included in is a basis of the subgroup that it generates.
Cite
@article{arxiv.1308.4260,
title = {Acyclic, connected and tree sets},
author = {Valerie Berthé and Clelia De Felice and Francesco Dolce and Julien Leroy and Dominique Perrin and Christophe Reutenauer and Giuseppina Rindone},
journal= {arXiv preprint arXiv:1308.4260},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1305.0127, arXiv:1011.5369, Monatsh. Math. (2015)