Algebraic characterization of dendricity
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911095553261568 |
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| author | Gheeraert, France Goulet-Ouellet, Herman Leroy, Julien Stas, Pierre |
| author_facet | Gheeraert, France Goulet-Ouellet, Herman Leroy, Julien Stas, Pierre |
| contents | Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every set of return words is a basis of the free group over the alphabet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic characterization of dendricity Gheeraert, France Goulet-Ouellet, Herman Leroy, Julien Stas, Pierre Discrete Mathematics Combinatorics Dynamical Systems Group Theory Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every set of return words is a basis of the free group over the alphabet. |
| title | Algebraic characterization of dendricity |
| topic | Discrete Mathematics Combinatorics Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2406.15075 |