A Proof of Rauzy's Conjecture on Abelian Complexity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909010511265792 |
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| author | Andrieu, Mélodie Vivion, Léo |
| author_facet | Andrieu, Mélodie Vivion, Léo |
| contents | A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity equal to 2. In this article, we prove a conjecture of Rauzy (1983), showing that there do not exist infinite ternary words with rationally independent letter frequencies and constant abelian complexity equal to 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01577 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Proof of Rauzy's Conjecture on Abelian Complexity Andrieu, Mélodie Vivion, Léo Combinatorics Dynamical Systems A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity equal to 2. In this article, we prove a conjecture of Rauzy (1983), showing that there do not exist infinite ternary words with rationally independent letter frequencies and constant abelian complexity equal to 3. |
| title | A Proof of Rauzy's Conjecture on Abelian Complexity |
| topic | Combinatorics Dynamical Systems |
| url | https://arxiv.org/abs/2605.01577 |