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- W4300107637 abstract "In this paper we consider the following question in the spirit of Ramsey theory: Given $xin A^omega,$ where $A$ is a finite non-empty set, does there exist a finite coloring of the non-empty factors of $x$ with the property that no factorization of $x$ 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 $A^omega.$ We also show that it has a positive answer for various classes of uniformly recurrent words, including all aperiodic balanced words, and all words $xin A^omega$ satisfying $lambda_x(n+1)-lambda_x(n)=1$ for all $n$ sufficiently large, where $ lambda_x(n)$ denotes the number of distinct factors of $x$ of length $n.$" @default.
- W4300107637 created "2022-10-03" @default.
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- W4300107637 date "2013-07-10" @default.
- W4300107637 modified "2023-10-16" @default.
- W4300107637 title "A Coloring Problem for Infinite Words" @default.
- W4300107637 doi "https://doi.org/10.48550/arxiv.1307.2828" @default.
- W4300107637 hasPublicationYear "2013" @default.
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