Abelian returns in Sturmian words
Formal Languages and Automata Theory
2011-08-19 v1 Discrete Mathematics
Combinatorics
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.
Cite
@article{arxiv.1108.3635,
title = {Abelian returns in Sturmian words},
author = {Svetlana Puzynina and Luca Q. Zamboni},
journal= {arXiv preprint arXiv:1108.3635},
year = {2011}
}
Comments
In Proceedings WORDS 2011, arXiv:1108.3412