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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.16283 |
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| _version_ | 1866913190503251968 |
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| author | Elmacioglu, Ceyhun Hilmer, Kieran O'Neill, Christopher Okandan, Melin Park-Kaufmann, Hannah |
| author_facet | Elmacioglu, Ceyhun Hilmer, Kieran O'Neill, Christopher Okandan, Melin Park-Kaufmann, Hannah |
| contents | In this paper, we consider the following question: "given the multiplicity $m$ and embedding dimension $e$ of a numerical semigroup $S$, what can be said about the cardinality $η$ of a minimal presentation of $S$?" We approach this question from a combinatorial (poset-theoretic) perspective, utilizing the recently-introduced notion of a Kunz nilsemigroup. In addition to making significant headway on this question beyond what was previously known, in the form of both explicit constructions and general bounds, we provide a self-contained introduction to Kunz nilsemigroups that avoids the polyhedral geometry necessary for much of their source material. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16283 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the cardinality of minimal presentations of numerical semigroups Elmacioglu, Ceyhun Hilmer, Kieran O'Neill, Christopher Okandan, Melin Park-Kaufmann, Hannah Combinatorics Commutative Algebra In this paper, we consider the following question: "given the multiplicity $m$ and embedding dimension $e$ of a numerical semigroup $S$, what can be said about the cardinality $η$ of a minimal presentation of $S$?" We approach this question from a combinatorial (poset-theoretic) perspective, utilizing the recently-introduced notion of a Kunz nilsemigroup. In addition to making significant headway on this question beyond what was previously known, in the form of both explicit constructions and general bounds, we provide a self-contained introduction to Kunz nilsemigroups that avoids the polyhedral geometry necessary for much of their source material. |
| title | On the cardinality of minimal presentations of numerical semigroups |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2211.16283 |