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

Abstract

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 ≥ 4, a k-power-free uniform morphism is a (k + 1)-power-free morphism.