Etude des morphismes pr{\'e}servant les mots primitifs

TL;DR

This paper reviews properties of primitive words and morphisms that preserve them, providing proofs and new results on the primitiveness of certain morphisms, especially those without high powers.

Contribution

It introduces new criteria for primitive morphisms, showing that morphisms without certain powers are primitive, and offers a nearly self-contained overview of primitive words.

Findings

Morphisms without powers k(≥5) are primitive.

Uniform morphisms without powers k(≥2) are primitive.

Provides proofs and properties of primitive words and morphisms.

Abstract

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.