A Characterization of Overlap-Free Morphisms

We prove that a morphism h over a two-letter alphabet {a, b} is overlap-free, i.e., maps overlap-free words into overlap-free words, iff the word h(abbabaab) is overlap-free. As a consequence, we obtain a simple proof of the fact that the only infinite overlap-free words that can be obtained by iterating a morphism are the Thue-Morse sequence and its opposite. RLsumP Nous prouvons qu’un morphisme h sur un alphabet a deux lettres {a, b} est sans chevauchement, c’est-a-dire envoie les mots sans chevauchement sur des mots sans chevauchement si et seulement si le mot h(abbabaab) est sans chevauchement. Comme consequence, nous obtenons une preuve simple du fait que les seuls mots infinis sans chevauchement qui peuvent &tre obtenus par iteration dun morphisme sont le mot de Thue-Morse et son oppose.