Acyclic, connected and tree sets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Monatshefte für Mathematik Année : 2014

Acyclic, connected and tree sets

Résumé

Given a set S of words, one associates to each word w in S an undi-rected graph, called its extension graph, and which describes the possible extensions of w in S 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 exhibit for this family various connexions between word combinatorics, bifix codes, group automata and free groups. 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 S is acyclic if and only if any bifix code included in S is a basis of the subgroup that it generates.
Fichier principal
Vignette du fichier
acyclicConnectedTreeArXivFinal.pdf (284.67 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01121887 , version 1 (02-03-2015)

Identifiants

Citer

Valérie Berthé, Clelia de Felice, Francesco Dolce, Julien Leroy, Dominique Perrin, et al.. Acyclic, connected and tree sets. Monatshefte für Mathematik, 2014, ⟨10.1007/s00605-014-0721-4⟩. ⟨hal-01121887⟩
136 Consultations
265 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More