| Issue |
RAIRO-Theor. Inf. Appl.
Volume 48, Number 4, October-December 2014
Special issue in the honor of the 14th "Journées Montoises d'Informatique Théorique". II.
|
|
|---|---|---|
| Page(s) | 467 - 478 | |
| DOI | https://doi.org/10.1051/ita/2014020 | |
| Published online | 31 July 2014 | |
5-Abelian cubes are avoidable on binary alphabets∗,∗∗
1
Christian-Albrechts-Universität zu Kiel, Institut für Informatik,
24098
Kiel,
Germany
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2
Department of Mathematics and Statistics, University of
Turku, 20014
Turku,
Finland
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Received: 14 March 2014
Accepted: 19 March 2014
Abstract
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.
Mathematics Subject Classification: 68Q70 / 68R15
Key words: Combinatorics on words / k-abelian equivalence / repetition-freeness / cube-freeness
Supported by the Alexander von Humboldt Foundation while author was affiliated at Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, PSF 4120, 39016 Magdeburg, Germany.
Supported by the Academy of Finland under grants 137991 (FiDiPro) and 257857.
© EDP Sciences 2014
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