English

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

R2 v1 2026-06-21T18:52:11.507Z