Words avoiding the morphic images of most of their factors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912616547352576 |
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| author | Ochem, Pascal Rosenfeld, Matthieu |
| author_facet | Ochem, Pascal Rosenfeld, Matthieu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Words avoiding the morphic images of most of their factors Ochem, Pascal Rosenfeld, Matthieu Combinatorics 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. |
| title | Words avoiding the morphic images of most of their factors |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.13368 |