Construction of a bi-infinite power free word with a given factor and a non-recurrent letter

02/24/2022

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by   Josef Rukavicka, et al.

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Let L_k,α^ℤ denote the set of all bi-infinite α-power free words over an alphabet with k letters, where α is a positive rational number and k is positive integer. We prove that if α≥ 5, k≥ 3, v∈ L_k,α^ℤ, and w is a finite factor of v, then there are v∈ L_k,α^ℤ and a letter x such that w is a factor of v and x has only a finitely many occurrences in v.