Numerical semigroup tree: type-representation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915634219057152 |
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| author | Chappelon, Jonathan Alfonsín, Jorge L. Ramírez Stamate, Dumitru I. |
| author_facet | Chappelon, Jonathan Alfonsín, Jorge L. Ramírez Stamate, Dumitru I. |
| contents | In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of genus $g$ and type $t$ is constante when $t$ is close to $g$ while $g$ grows. We also study the unimodality of various sequences as well as the behavior of the leaves in $\mathcal T$. We put forward several conjectures that are supported by various computational experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical semigroup tree: type-representation Chappelon, Jonathan Alfonsín, Jorge L. Ramírez Stamate, Dumitru I. Commutative Algebra 05A15, 11D07, 05E40, In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of genus $g$ and type $t$ is constante when $t$ is close to $g$ while $g$ grows. We also study the unimodality of various sequences as well as the behavior of the leaves in $\mathcal T$. We put forward several conjectures that are supported by various computational experiments. |
| title | Numerical semigroup tree: type-representation |
| topic | Commutative Algebra 05A15, 11D07, 05E40, |
| url | https://arxiv.org/abs/2507.15006 |