A Coloring Problem for Sturmian and Episturmian Words

Aldo de Luca, Elena V. Pribavkina, Luca Q. Zamboni

Published 2013-01-22Version 1

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