no. 4
5-abelian cubes are avoidable on binary alphabets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 467-478

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.

DOI : 10.1051/ita/2014020
Classification : 68Q70, 68R15
Keywords: combinatorics on words, k-abelian equivalence, repetition-freeness, cube-freeness 
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Mercaş, Robert; Saarela, Aleksi. 5-abelian cubes are avoidable on binary alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 467-478. doi: 10.1051/ita/2014020

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