On some classes of generalized numerical semigroups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916662389768192 |
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| author | Cisto, Carmelo Navarra, Francesco |
| author_facet | Cisto, Carmelo Navarra, Francesco |
| contents | A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first class satisfies a generalization of Wilf's conjecture, by introducing a generalization of a well-known sufficient condition for Wilf's conjecture in numerical semigroups, that involves the type of the semigroup. Partial results for Wilf's generalized conjecture are obtained also for the other two classes, and some open questions are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12467 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On some classes of generalized numerical semigroups Cisto, Carmelo Navarra, Francesco Combinatorics 20M14, 11D07 A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first class satisfies a generalization of Wilf's conjecture, by introducing a generalization of a well-known sufficient condition for Wilf's conjecture in numerical semigroups, that involves the type of the semigroup. Partial results for Wilf's generalized conjecture are obtained also for the other two classes, and some open questions are provided. |
| title | On some classes of generalized numerical semigroups |
| topic | Combinatorics 20M14, 11D07 |
| url | https://arxiv.org/abs/2212.12467 |