Length-k-overlap-free Binary Infinite Words
We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with vertical bar x vertical bar  = 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.
infinite words partial words repetition-freeness length-k-overlaps thue-morse word