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5-Abelian cubes are avoidable on binary alphabets∗∗∗

Published online by Cambridge University Press:  31 July 2014

Robert Mercaş  and
Aleksi Saarela
Robert Mercaş
Affiliation:
Christian-Albrechts-Universität zu Kiel, Institut für Informatik, 24098 Kiel, Germany. rgm@informatik.uni-kiel.de
Aleksi Saarela
Affiliation:
Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland; amsaar@utu.fi
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Abstract

A k-abeliancube is a word uvw, where the factors u, v, and w are either pairwiseequal, or have the same multiplicities for every one of their factors of length at mostk.Previously it has been shown that k-abelian cubes are avoidable over a binaryalphabet for k ≥8. Here it is proved that this holds for k ≥ 5.

Keywords

Combinatorics on wordsk-abelianequivalencerepetition-freenesscube-freeness

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