On minimal presentations of numerical monoids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909608068513792 |
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| author | Moscariello, Alessio Sammartano, Alessio |
| author_facet | Moscariello, Alessio Sammartano, Alessio |
| contents | We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing this problem, we apply tools from Hilbert functions and free resolutions of artinian standard graded algebras. This approach allows us to solve the problem in many cases and, at the same time, identify subtle difficulties in the remaining cases. As a by-product of our analysis, we deduce results for the corresponding problem for the type of a numerical monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On minimal presentations of numerical monoids Moscariello, Alessio Sammartano, Alessio Combinatorics Commutative Algebra 20M14, 05E40, 13D02, 13F55, 13F65 We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing this problem, we apply tools from Hilbert functions and free resolutions of artinian standard graded algebras. This approach allows us to solve the problem in many cases and, at the same time, identify subtle difficulties in the remaining cases. As a by-product of our analysis, we deduce results for the corresponding problem for the type of a numerical monoid. |
| title | On minimal presentations of numerical monoids |
| topic | Combinatorics Commutative Algebra 20M14, 05E40, 13D02, 13F55, 13F65 |
| url | https://arxiv.org/abs/2405.19810 |