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Words avoiding the morphic images of most of their factors
Article de revue   Open Access   Avec comité de lecture

Words avoiding the morphic images of most of their factors

Pascal Ochem et Matthieu Rosenfeld
Discrete Mathematics and Theoretical Computer Science, Vol.27:3(Combinatorics)
23/09/2025

Résumé

Combinatorics on words
We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite word contains an imaged factor of length at least 6 and that 6 is best possible. We show that every infinite binary word contains at least 36 distinct imaged factors and that 36 is best possible.

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