Avoiding approximate repetitions with respect to the longest common subsequence distance

Camungol, Serina; Rampersad, Narad

doi:10.2140/involve.2016.9.657

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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

DOI: 10.2140/involve.2016.9.657

Abstract

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 $x x^{'}$ , 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.

Keywords

approximate repetition, longest common subsequence, entropy compression

Mathematical Subject Classification 2010

Primary: 68R15

Milestones

Received: 20 March 2015

Revised: 6 September 2015

Accepted: 17 September 2015

Published: 6 July 2016

Communicated by Joshua Cooper

Authors

Serina Camungol
Department of Mathematics and Statistics University of Winnipeg 515 Portage Ave. Winnipeg MB R3B 2E9 Canada

Narad Rampersad
Department of Mathematics and Statistics University of Winnipeg 515 Portage Ave. Winnipeg MB R3B 2E9 Canada

Vol. 9, No. 4, 2016