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5-Abelian cubes are avoidable on binary alphabets ∗∗∗
Robert Mercaş, Aleksi Saarela
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 4 / October 2014

Published online by Cambridge University Press:

31 July 2014, pp. 467-478

Print publication:

October 2014
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A k-abelian cube is a word uvw, where the factors u, v, and w are either pairwise equal, or have the same multiplicities for every one of their factors of length at most k. Previously it has been shown that k-abelian cubes are avoidable over a binary alphabet for k ≥ 8. Here it is proved that this holds for k ≥ 5.