A uniform cube-free morphism isk-power-free for all integersk≥ 4
Francis Wlazinski · RAIRO - Theoretical Informatics and Applications · 2017
In the study ofk-power-free morphisms, the case of 3-free-morphisms,i.e., cube-free morphisms, often differs from otherk-power-free morphisms. Indeed, cube-freeness is less restrictive than square-freeness. And a cube provides less equations to solve than any integerk≥ 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 ak-power-free morphism for all integersk≥ 4.