A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Abelian returns in Sturmian words

Julkaisun tekijät: S Puzynina, L Q Zamboni
Kustantaja: elsevier
Julkaisuvuosi: 2013
Journal: Journal of Combinatorial Theory, Series A
Numero sarjassa: 2
Volyymi: 120
Julkaisunumero: 2
ISSN: 0097-3165


Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the ¯rst 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 in¯nite 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.

Last updated on 2019-21-08 at 23:30