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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.12195 |
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| _version_ | 1866912160620216320 |
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| author | Blasco-García, Rubén Cumplido, María Holt, Derek F. Morris-Wright, Rose Rees, Sarah |
| author_facet | Blasco-García, Rubén Cumplido, María Holt, Derek F. Morris-Wright, Rose Rees, Sarah |
| contents | We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco-García, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rewriting in Artin groups without A_3 or B_3 subdiagrams Blasco-García, Rubén Cumplido, María Holt, Derek F. Morris-Wright, Rose Rees, Sarah Group Theory 20F36, 20F10 (Primary) 68R15 (Secondary) We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco-García, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively. |
| title | Rewriting in Artin groups without A_3 or B_3 subdiagrams |
| topic | Group Theory 20F36, 20F10 (Primary) 68R15 (Secondary) |
| url | https://arxiv.org/abs/2412.12195 |