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Ochem, Rampersad, and Shallit gave various examples of infinite wordsavoiding what they called approximate repetitions. An approximate repetition isa factor of the form xx', where x and x' are close to being identical. In theirwork, they measured the similarity of x and x' using either the Hammingdistance or the edit distance. In this paper, we show the existence of wordsavoiding approximate repetitions, where the measure of similarity betweenadjacent factors is based on the length of the longest common subsequence. Ourprincipal technique is the so-called "entropy compression" method, which hasits origins in Moser and Tardos's algorithmic version of the Lovasz locallemma.

Avoiding approximate repetitions with respect to the longest common subsequence distance