Reduction in non-($k+1$)-power-free morphisms

Wlazinski, Francis

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 3-20.

Under some hypotheses, if the image by a morphism of a $(k+1)$-power-free word contains a $(k+1)$-power, we can reduce this word to obtain a new word with the same scheme. These hypotheses are satisfied in the case of uniform morphisms. This allows us to state that, when $k\ge 4$, a $k$-power-free uniform morphism is a $(k+1)$-power-free morphism.

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