Numerical Semigroups with $a_e = 2g+1$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915952678928384 |
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| author | Hellus, Michael Hübl, Reinhold Rechenauer, Anton |
| author_facet | Hellus, Michael Hübl, Reinhold Rechenauer, Anton |
| contents | This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be $2g+1$, where $g$ is the genus of the semigroup. We will show that these semigroups are closely related to symmetric semigroups and have interesting symmetry properties themselves. Furthermore we will show that Wilf's question has a positive answer for these semigroups and some semigroups derived thereof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21948 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerical Semigroups with $a_e = 2g+1$ Hellus, Michael Hübl, Reinhold Rechenauer, Anton Group Theory Commutative Algebra Number Theory 13H10, 13F20, 11D07, 20M14 This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be $2g+1$, where $g$ is the genus of the semigroup. We will show that these semigroups are closely related to symmetric semigroups and have interesting symmetry properties themselves. Furthermore we will show that Wilf's question has a positive answer for these semigroups and some semigroups derived thereof. |
| title | Numerical Semigroups with $a_e = 2g+1$ |
| topic | Group Theory Commutative Algebra Number Theory 13H10, 13F20, 11D07, 20M14 |
| url | https://arxiv.org/abs/2604.21948 |