Rarity of the infinite chains in the tree of numerical semigroups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917579750113280 |
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| author | Bras-Amorós, Maria Ribeiro, Mariana Rosas |
| author_facet | Bras-Amorós, Maria Ribeiro, Mariana Rosas |
| contents | We prove that, for each fixed genus, the portion of semigroups of that
genus belonging to infinite chains in the semigroup tree approaches 0 as
the genus grows to infinite. This means that most numerical semigroups
have a finite number of descendants in the semigroup tree. This problem
has been open since 2009. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_18060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rarity of the infinite chains in the tree of numerical semigroups Bras-Amorós, Maria Ribeiro, Mariana Rosas Number Theory Discrete Mathematics Combinatorics 68W30, 06F05, 20M14, 05A99 We prove that, for each fixed genus, the portion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinite. This means that most numerical semigroups have a finite number of descendants in the semigroup tree. This problem has been open since 2009. |
| title | Rarity of the infinite chains in the tree of numerical semigroups |
| topic | Number Theory Discrete Mathematics Combinatorics 68W30, 06F05, 20M14, 05A99 |
| url | https://arxiv.org/abs/2401.18060 |