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We consider a recently defined notion of k-abelian equivalence of words by concentrating on avoidance problems. The equivalence class of a word depends on the numbers of occurrences of different factors of length k for a fixed natural number k and the prefix of the word. We have shown earlier that over a ternary alphabet k-abelian squares cannot be avoided in pure morphic words for any natural number k. Nevertheless, computational experiments support the conjecture that even 3-abelian squares can be avoided over ternary alphabets. In this paper we establish the first avoidance result showing that by choosing k to be large enough we have an infinite k-abelian square-free word over three letter alphabet. In addition, this word can be obtained as a morphic image of a pure morphic word.
@article{ITA_2014__48_3_307_0,
author = {Huova, Mari},
title = {Existence of an infinite ternary 64-abelian square-free word},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {307--314},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/ita/2014012},
mrnumber = {3302490},
zbl = {1297.68192},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014012/}
}
TY - JOUR AU - Huova, Mari TI - Existence of an infinite ternary 64-abelian square-free word JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 307 EP - 314 VL - 48 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2014012/ DO - 10.1051/ita/2014012 LA - en ID - ITA_2014__48_3_307_0 ER -
%0 Journal Article %A Huova, Mari %T Existence of an infinite ternary 64-abelian square-free word %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 307-314 %V 48 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2014012/ %R 10.1051/ita/2014012 %G en %F ITA_2014__48_3_307_0
Huova, Mari. Existence of an infinite ternary 64-abelian square-free word. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 307-314. doi: 10.1051/ita/2014012
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