Vol. 9, No. 4, 2016

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Avoiding approximate repetitions with respect to the longest common subsequence distance

Serina Camungol and Narad Rampersad

Vol. 9 (2016), No. 4, 657–666

Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form xx, where x and x are close to being identical. In their work, they measured the similarity of x and x using either the Hamming distance or the edit distance. In this paper, we show the existence of words avoiding approximate repetitions, where the measure of similarity between adjacent factors is based on the length of the longest common subsequence. Our principal technique is the so-called “entropy compression” method, which has its origins in Moser and Tardos’s algorithmic version of the Lovász local lemma.

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approximate repetition, longest common subsequence, entropy compression
Mathematical Subject Classification 2010
Primary: 68R15
Received: 20 March 2015
Revised: 6 September 2015
Accepted: 17 September 2015
Published: 6 July 2016

Communicated by Joshua Cooper
Serina Camungol
Department of Mathematics and Statistics
University of Winnipeg
515 Portage Ave.
Winnipeg MB R3B 2E9
Narad Rampersad
Department of Mathematics and Statistics
University of Winnipeg
515 Portage Ave.
Winnipeg MB R3B 2E9