Half-flips are 5-avoidable
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917509476646912 |
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| author | Ochem, Pascal |
| author_facet | Ochem, Pascal |
| contents | A word contains a \emph{half-flip} if it contains non-empty factors $uv$ and $vu$ where $|u|=|v|$. Fici reports a non-constructive proof of the existence of an infinite word over a finite alphabet avoiding half-flips and asks for the size of the smallest alphabet over which half-flips may be avoided. Currie and Rampersad have proposed a pure morphic word over 8 letters and a morphic word over 5 letters and conjecture that they avoid half-flips. We present a pure morphic word over 5 letters that avoids half-flips. We also show that half-flips with $|u|\ge2$ are 3-avoidable and that half-flips with $|u|\ge4$ are 2-avoidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18811 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Half-flips are 5-avoidable Ochem, Pascal Combinatorics Formal Languages and Automata Theory A word contains a \emph{half-flip} if it contains non-empty factors $uv$ and $vu$ where $|u|=|v|$. Fici reports a non-constructive proof of the existence of an infinite word over a finite alphabet avoiding half-flips and asks for the size of the smallest alphabet over which half-flips may be avoided. Currie and Rampersad have proposed a pure morphic word over 8 letters and a morphic word over 5 letters and conjecture that they avoid half-flips. We present a pure morphic word over 5 letters that avoids half-flips. We also show that half-flips with $|u|\ge2$ are 3-avoidable and that half-flips with $|u|\ge4$ are 2-avoidable. |
| title | Half-flips are 5-avoidable |
| topic | Combinatorics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2605.18811 |