A Coloring Problem for Sturmian and Episturmian Words
classification
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cs.DM
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coloringwordepisturmiansturmianalwaysaperiodicconsiderexist
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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.
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