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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.
@article{ITA_2014__48_4_467_0,
author = {Merca\c{s}, Robert and Saarela, Aleksi},
title = {5-abelian cubes are avoidable on binary alphabets},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {467--478},
publisher = {EDP-Sciences},
volume = {48},
number = {4},
year = {2014},
doi = {10.1051/ita/2014020},
mrnumber = {3302498},
zbl = {1302.68229},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014020/}
}
TY - JOUR AU - Mercaş, Robert AU - Saarela, Aleksi TI - 5-abelian cubes are avoidable on binary alphabets JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 467 EP - 478 VL - 48 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2014020/ DO - 10.1051/ita/2014020 LA - en ID - ITA_2014__48_4_467_0 ER -
%0 Journal Article %A Mercaş, Robert %A Saarela, Aleksi %T 5-abelian cubes are avoidable on binary alphabets %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 467-478 %V 48 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2014020/ %R 10.1051/ita/2014020 %G en %F ITA_2014__48_4_467_0
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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