Stability properties for subgroups generated by return words
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909727583109120 |
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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 | Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stability for subgroups generated by return words. Within this framework, we revisit several existing results and generalize some of them. We also study general aspects of stability, such as decidability or closure under certain operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability properties for subgroups generated by return words Gheeraert, France Goulet-Ouellet, Herman Leroy, Julien Stas, Pierre Discrete Mathematics Combinatorics Dynamical Systems Group Theory 37B10 (Primary) 68R15 (Secondary) Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stability for subgroups generated by return words. Within this framework, we revisit several existing results and generalize some of them. We also study general aspects of stability, such as decidability or closure under certain operations. |
| title | Stability properties for subgroups generated by return words |
| topic | Discrete Mathematics Combinatorics Dynamical Systems Group Theory 37B10 (Primary) 68R15 (Secondary) |
| url | https://arxiv.org/abs/2410.12534 |