Abelian returns in Sturmian words - Archive ouverte HAL
Article Dans Une Revue Journal of Combinatorial Theory, Series A Année : 2013

Abelian returns in Sturmian words

Svetlana Puzynina
  • Fonction : Auteur
Luca Q. Zamboni
  • Fonction : Auteur
  • PersonId : 902187

Résumé

Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the first return map in dynamical systems. In this paper we investigate two abelian variants of the notion of return word, each of them gives rise to a new characterization of Sturmian words. We prove that a recurrent infinite word is Sturmian if and only if each of its factors has two or three abelian (or semi-abelian) returns. We study the structure of abelian returns in Sturmian words and give a characterization of those factors having exactly two abelian returns. Finally we discuss connections between abelian returns and periodicity in words.

Dates et versions

hal-00865197 , version 1 (24-09-2013)

Identifiants

Citer

Svetlana Puzynina, Luca Q. Zamboni. Abelian returns in Sturmian words. Journal of Combinatorial Theory, Series A, 2013, 120 (2), pp.390-408. ⟨10.1016/j.jcta.2012.09.002⟩. ⟨hal-00865197⟩
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