On numerical semigroups with embedding dimension four
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910259964018688 |
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| author | Chomicz, Kazimierz |
| author_facet | Chomicz, Kazimierz |
| contents | We develop a geometric procedure for finding the Apéry set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We illustrate our method by finding the Frobenius numbers, genera, Betti elements, minimal presentations, and catenary degrees of numerical semigroups generated by four consecutive squares and by four consecutive triangular numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On numerical semigroups with embedding dimension four Chomicz, Kazimierz Number Theory 11D07, 20M13, 20M14 We develop a geometric procedure for finding the Apéry set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We illustrate our method by finding the Frobenius numbers, genera, Betti elements, minimal presentations, and catenary degrees of numerical semigroups generated by four consecutive squares and by four consecutive triangular numbers. |
| title | On numerical semigroups with embedding dimension four |
| topic | Number Theory 11D07, 20M13, 20M14 |
| url | https://arxiv.org/abs/2604.25653 |