Low complexity binary words avoiding $(5/2)^+$-powers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914105624887296 |
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| author | Currie, James Rampersad, Narad |
| author_facet | Currie, James Rampersad, Narad |
| contents | Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid $(5/2)^+$-powers, confirming a conjecture of Ollinger and Shallit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low complexity binary words avoiding $(5/2)^+$-powers Currie, James Rampersad, Narad Combinatorics Formal Languages and Automata Theory 68R15 Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid $(5/2)^+$-powers, confirming a conjecture of Ollinger and Shallit. |
| title | Low complexity binary words avoiding $(5/2)^+$-powers |
| topic | Combinatorics Formal Languages and Automata Theory 68R15 |
| url | https://arxiv.org/abs/2506.19050 |