Abelian returns in Sturmian words

Svetlana Puzynina
(University of Turku, Finland; and Sobolev Institute of Mathematics, Novosibirsk, Russia)
Luca Q. Zamboni
(Universite de Lyon, France; and University of Turku, Finland)

In this paper we study an abelian version of the notion of return word. Our main result is a new characterization of Sturmian words via abelian returns. Namely, we prove that a word is Sturmian if and only if each of its factors has two or three abelian returns. In addition, we describe the structure of abelian returns in Sturmian words, and discuss connections between abelian returns and periodicity.

In Petr Ambrož, Štěpán Holub and Zuzana Masáková: Proceedings 8th International Conference Words 2011 (WORDS 2011), Prague, Czech Republic, 12-16th September 2011, Electronic Proceedings in Theoretical Computer Science 63, pp. 179–188.
Published: 17th August 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.63.24 bibtex PDF
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