A Combinatorial Proof of S-adicity for Sequences with Linear Complexity

Julien Leroy 1 Gwenaël Richomme 2, 3
1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 UM3 - Université Paul-Valéry - Montpellier 3
3 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Using Rauzy graphs, Ferenczi proved that if a symbolic dynamical system has linear complexity then it is S-adic. Being more specific, the result can also be proved for infinite words. We provide a new proof of this latter result using the notion of return words to a set of words.
Keywords : uniform recurrence factor complexity S-adicity S-adic conjecture subword complexity morphism linear complexity
Type de document :
Article dans une revue
Integers : Electronic Journal of Combinatorial Number Theory, State University of West Georgia, Charles University, and DIMATIA, 2013, 13, pp.article #A5. 〈http://www.integers-ejcnt.org/vol13.html〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00797658
Contributeur : Gwenaël Richomme <>
Soumis le : jeudi 7 mars 2013 - 08:36:01
Dernière modification le : mercredi 11 juillet 2018 - 21:04:38

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Julien Leroy, Gwenaël Richomme. A Combinatorial Proof of S-adicity for Sequences with Linear Complexity. Integers : Electronic Journal of Combinatorial Number Theory, State University of West Georgia, Charles University, and DIMATIA, 2013, 13, pp.article #A5. 〈http://www.integers-ejcnt.org/vol13.html〉. 〈lirmm-00797658〉

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