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摘要
In this paper we consider the following question in the spirit of Ramsey theory: Given x epsilon 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 x epsilon A(omega) satisfying lambda(x) (n + 1) - lambda(n) = 1 for all n sufficiently large, where lambda(x) (n) denotes the number of distinct factors of x of length n.
- 出版日期2014-7
