In the study of k-power-free morphisms, the case of 3-free-morphisms, i.e., cube-free morphisms, often differs from other k-power-free morphisms. Indeed, cube-freeness is less restrictive than square-freeness. And a cube provides less equations to solve than any integer k ≥ 4. Anyway, the fact that the image of a word by a morphism contains a cube implies relations that, under some assumptions, allow us to establish our main result: a cube-free uniform morphism is a k-power-free morphism for all integers k ≥ 4.
DOI : 10.1051/ita/2017015
Mots clés : Morphisms, repetition, cube, k-power
@article{ITA_2017__51_4_205_0,
author = {Wlazinski, Francis},
editor = {Leroy, J. and Rigo, M. and Charlier, E.},
title = {A uniform cube-free morphism is k-power-free for all integers k \ensuremath{\geq} 4},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {205--216},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/ita/2017015},
mrnumber = {3782821},
zbl = {1453.68147},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2017015/}
}
TY - JOUR AU - Wlazinski, Francis ED - Leroy, J. ED - Rigo, M. ED - Charlier, E. TI - A uniform cube-free morphism is k-power-free for all integers k ≥ 4 JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2017 SP - 205 EP - 216 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2017015/ DO - 10.1051/ita/2017015 LA - en ID - ITA_2017__51_4_205_0 ER -
%0 Journal Article %A Wlazinski, Francis %E Leroy, J. %E Rigo, M. %E Charlier, E. %T A uniform cube-free morphism is k-power-free for all integers k ≥ 4 %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2017 %P 205-216 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2017015/ %R 10.1051/ita/2017015 %G en %F ITA_2017__51_4_205_0
Wlazinski, Francis. A uniform cube-free morphism is k-power-free for all integers k ≥ 4. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 4, pp. 205-216. doi : 10.1051/ita/2017015. http://www.numdam.org/articles/10.1051/ita/2017015/
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