Generalized Numerical semigroups up to isomorphism
Fuente:
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_ | 1866915272053489664 |
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| author | Cisto, Carmelo Failla, Gioia Navarra, Francesco |
| author_facet | Cisto, Carmelo Failla, Gioia Navarra, Francesco |
| contents | A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that identifies the monoids obtained by the action of a permutation and establishing a criterion to select a representative from each equivalence class, we define some procedures for generating the set of all generalized numerical semigroups of given genus up to isomorphism. Finally, we present computational data and explore properties related to the number of generalized numerical semigroups of a given genus up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Numerical semigroups up to isomorphism Cisto, Carmelo Failla, Gioia Navarra, Francesco Combinatorics Commutative Algebra 20M14, 05A15, 11D07, 20-04 A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that identifies the monoids obtained by the action of a permutation and establishing a criterion to select a representative from each equivalence class, we define some procedures for generating the set of all generalized numerical semigroups of given genus up to isomorphism. Finally, we present computational data and explore properties related to the number of generalized numerical semigroups of a given genus up to isomorphism. |
| title | Generalized Numerical semigroups up to isomorphism |
| topic | Combinatorics Commutative Algebra 20M14, 05A15, 11D07, 20-04 |
| url | https://arxiv.org/abs/2409.14868 |