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A3 Book chapter

Minimal Similarity Relations for Square-Free Words

List of Authors: T. Harju, T. Kärki

Place: Bucharest

Publication year: 2014

Book title *: Discrete Mathematics and Computer Science. In Memoriam Alexandru Mateescu (1952-2005)

ISBN: 978-973-27-2470-5

Abstract

A relation R on words is a similarity relation if it is reflexive, symmetric and it is generated by letters. A word w is said to be R-square–free, if it has no factors of the form uv where u and v are related by R. We give a new proof for the result of Kärki [Fund. Inform., 116 (2012)] that the smallest similarity relation that gives an infinite square–free word is generated by six pairs.We also characterize all trees of order six corresponding to the similarity relations that admit a square–free word.

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