Abelian returns in Sturmian words

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Other literature type 17 Aug 2011Embargo end date: 01 Aug 2011 France English Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series A, volume 120, pages 390-408 (issn: 0097-3165,

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Authors: Puzynina, Svetlana; Zamboni, Luca Q.;

doi: 10.1016/j.jcta.2012.09.002 , 10.4204/eptcs.63.24 , 10.48550/arxiv.1108.3635 , 10.48550/arxiv.1204.5755

arXiv: 1204.5755 , 1108.3635

Abelian returns in Sturmian words

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Abstract

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 Proceedings WORDS 2011, arXiv:1108.3412

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France

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Keywords

FOS: Computer and information sciences, Return word, Discrete Mathematics (cs.DM), Formal Languages and Automata Theory (cs.FL), ta111, Sturmian word, Computer Science - Formal Languages and Automata Theory, QA75.5-76.95, 68R15, 004, Theoretical Computer Science, Abelian equivalence, Computational Theory and Mathematics, Electronic computers. Computer science, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], QA1-939, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics, Computer Science - Discrete Mathematics

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