Computing least common multiples in monoids with a finite Garside family
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917410755313664 |
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| author | Melliti, Emir |
| author_facet | Melliti, Emir |
| contents | Right-reversing is an algorithm used to compute least common multiples in monoids that admit a right-complemented presentation. The algorithm can either terminate and find a result, fail, or run indefinitely. The correctness of the algorithm can be proved with additional assumptions coming from Garside theory. In the same framework, we prove that a non-terminating run of the algorithm is necessarily cyclic. Stopping when a cycle is detected provides a way of computing a minimal Garside family. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing least common multiples in monoids with a finite Garside family Melliti, Emir Group Theory 20F36, 20M05 (Primary) 20F05, 20F10, 20M13 (Secondary) Right-reversing is an algorithm used to compute least common multiples in monoids that admit a right-complemented presentation. The algorithm can either terminate and find a result, fail, or run indefinitely. The correctness of the algorithm can be proved with additional assumptions coming from Garside theory. In the same framework, we prove that a non-terminating run of the algorithm is necessarily cyclic. Stopping when a cycle is detected provides a way of computing a minimal Garside family. |
| title | Computing least common multiples in monoids with a finite Garside family |
| topic | Group Theory 20F36, 20M05 (Primary) 20F05, 20F10, 20M13 (Secondary) |
| url | https://arxiv.org/abs/2604.13989 |