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We consider the following open question in the spirit of Ramsey theory: Givenan aperiodic infinite word $w$, does there exist a finite coloring of itsfactors such that no factorization of $w$ is monochromatic? We show that such acoloring always exists whenever $w$ is a Sturmian word or a standardepisturmian word.

A Coloring Problem for Sturmian and Episturmian Words