|Publication ahead of print|
RAIRO-Theor. Inf. Appl.
|Published online||13 February 2018|
A uniform cube-free morphism is k-power-free for all integers k ≥ 4
L.A.M.F.A., UMR 7352 du CNRS, Université de Picardie Jules Verne,
33 rue Saint-Leu,
Amiens Cedex 1, France
* Corresponding author: email@example.com
Accepted: 4 December 2017
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.
Mathematics Subject Classification: 68R15
Key words: Morphisms / repetition / cube / k-power
© EDP Sciences, 2018
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