A Class of Numerical Semigroups Defined by Kunz and Waldi
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910434809872384 |
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| author | Singh, Srishti Srinivasan, Hema |
| author_facet | Singh, Srishti Srinivasan, Hema |
| contents | In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers $p < q$, which we call KW semigroups. We characterize KW numerical semigroups by their principal matrices. We present a necessary and sufficient criterion for a matrix to be the principal matrix of a KW semigroup. An explicit description of the minimal resolutions of numerical semigroups in the same class with small embedding dimensions 3 and 4 is given. We give a generalization of this notion to three dimensions using lattice paths under a plane and present some preliminary results and questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Class of Numerical Semigroups Defined by Kunz and Waldi Singh, Srishti Srinivasan, Hema Commutative Algebra 13c05, 13c70, 13d02 In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers $p < q$, which we call KW semigroups. We characterize KW numerical semigroups by their principal matrices. We present a necessary and sufficient criterion for a matrix to be the principal matrix of a KW semigroup. An explicit description of the minimal resolutions of numerical semigroups in the same class with small embedding dimensions 3 and 4 is given. We give a generalization of this notion to three dimensions using lattice paths under a plane and present some preliminary results and questions. |
| title | A Class of Numerical Semigroups Defined by Kunz and Waldi |
| topic | Commutative Algebra 13c05, 13c70, 13d02 |
| url | https://arxiv.org/abs/2405.00331 |