An overlap-free morphism is a k-power-free morphism for any integer k $\ge$ 3
We show that any overlap-free morphism is a $k$-power-free morphism for all integers $k\geq 3$.
cs.FL↗
arXiv subjects
Francis Wlazinski
Publications and source records attributed to Francis Wlazinski.
Etude des morphismes pr{é}servant les mots primitifs
This article provides a reminder of some properties of primitive words and the morphisms that preserve them. Their proofs, which I have more or less revised, are included. This makes the article almost self-contained. I also contribute by giving some properties of primitive words, but especially by showing that a morphism without powers k($\ge$ 5) is primitive and that a uniform morphism without powers k($\ge$ 2) is primitive.
cs.FL↗
3-anti-power uniform morphisms
Words whose three successive factors of the same length are all different i.e. 3-anti-power words are a natural extension of square-free words (two successive factors of the same length are different). We give a way to verify whether a uniform morphism preserves 3-anti-power words (the image of a 3-anti-power word is a 3-anti-power word). A consequence of the existence of such morphisms is the possibility of generating an infinite 3-anti-power word.
cs.FL↗
Existence of finite test-sets for k-power-freeness of uniform morphisms
A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. We provide such an algorithm when k >= 3 for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite test-sets for k-power-freeness.
cs.DM↗