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Length-k-overlap-free Binary Infinite Words

Séébold P.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

251-263

We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k-1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k-1)-overlap-free. As an application, we prove that, for every non-negative integer n, there exist infinitely many length-k-overlap-free binary infinite partial words with n holes.