Abelian returns in Sturmian words

Details Abelian returns in Sturmian words Abelian returns in Sturmian words

2011-08-18

arxiv.org/abs/1108.3635v1

EPTCS 63, 2011, pp. 179-188

Computer Science

Formal Languages and Automata Theory

In Proceedings WORDS 2011, arXiv:1108.3412

Scientific paper

10.4204/EPTCS.63.24

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.

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