Numerical Semigroups of Sally Type II
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908705791934464 |
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| author | Goel, Kriti Şahin, Nil Singh, Srishti Srinivasan, Hema |
| author_facet | Goel, Kriti Şahin, Nil Singh, Srishti Srinivasan, Hema |
| contents | In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $ν\ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We also construct a minimal resolution for another special class of such semigroups of type $ν-1$. Finally, we propose some conjectures for the Betti numbers of families of non-symmetric Sally type semigroups in the above cases in relation to those of the corresponding Gorenstein cases of Sally type semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Semigroups of Sally Type II Goel, Kriti Şahin, Nil Singh, Srishti Srinivasan, Hema Commutative Algebra 13D02, 13D05, 20M14, 13H10 In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $ν\ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We also construct a minimal resolution for another special class of such semigroups of type $ν-1$. Finally, we propose some conjectures for the Betti numbers of families of non-symmetric Sally type semigroups in the above cases in relation to those of the corresponding Gorenstein cases of Sally type semigroups. |
| title | Numerical Semigroups of Sally Type II |
| topic | Commutative Algebra 13D02, 13D05, 20M14, 13H10 |
| url | https://arxiv.org/abs/2512.10812 |