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A Coloring Problem for Infinite Words
In this paper we consider the following question in the spirit of Ramsey
theory: Given where is a finite non-empty set, does there
exist a finite coloring of the non-empty factors of with the property that
no factorization of is monochromatic? We prove that this question has a
positive answer using two colors for almost all words relative to the standard
Bernoulli measure on We also show that it has a positive answer for
various classes of uniformly recurrent words, including all aperiodic balanced
words, and all words satisfying
for all sufficiently large, where denotes the number of
distinct factors of of length Comment: arXiv admin note: incorporates 1301.526
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