Work

Words avoiding the morphic images of most of their factors

Year: 2025

Type: article

Abstract: 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.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.15919

Authors: Pascal Ochem, Matthieu Rosenfeld

Institutions: Centre National de la Recherche Scientifique, Université de Montpellier, Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Counting Argument for Discret Objects