English

A Coloring Problem for Sturmian and Episturmian Words

Combinatorics 2013-01-23 v1 Discrete Mathematics

Abstract

We consider the following open question in the spirit of Ramsey theory: Given an aperiodic infinite word ww, does there exist a finite coloring of its factors such that no factorization of ww is monochromatic? We show that such a coloring always exists whenever ww is a Sturmian word or a standard episturmian word.

Keywords

Cite

@article{arxiv.1301.5263,
  title  = {A Coloring Problem for Sturmian and Episturmian Words},
  author = {Aldo de Luca and Elena V. Pribavkina and Luca Q. Zamboni},
  journal= {arXiv preprint arXiv:1301.5263},
  year   = {2013}
}
R2 v1 2026-06-21T23:13:39.321Z