Consecutive Power Occurrences in Sturmian Words
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909107226673152 |
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| author | Bell, Jason Schulz, Chris Shallit, Jeffrey |
| author_facet | Bell, Jason Schulz, Chris Shallit, Jeffrey |
| contents | We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is optimal, extending a result of Rampersad, who proved that the bound $9$ holds for the Fibonacci word. We then give a general result showing that for every $e \in [1,(5+\sqrt{5})/2)$ there is a natural number $N$, depending only on $e$, such that every Sturmian word has the property that the distance between consecutive ending positions of $e$-powers occurring in the word is uniformly bounded by $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consecutive Power Occurrences in Sturmian Words Bell, Jason Schulz, Chris Shallit, Jeffrey Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is optimal, extending a result of Rampersad, who proved that the bound $9$ holds for the Fibonacci word. We then give a general result showing that for every $e \in [1,(5+\sqrt{5})/2)$ there is a natural number $N$, depending only on $e$, such that every Sturmian word has the property that the distance between consecutive ending positions of $e$-powers occurring in the word is uniformly bounded by $N$. |
| title | Consecutive Power Occurrences in Sturmian Words |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory |
| url | https://arxiv.org/abs/2402.09597 |