The Frobenius problem for a class of quotients of numerical semigroups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918474012426240 |
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| author | Liu, Feihu |
| author_facet | Liu, Feihu |
| contents | Given a numerical semigroup $S$ and a positive integer $p$, the quotient $\frac{S}{p}=\{x\in \mathbb{N} \mid px\in S\}$ also forms a numerical semigroup. In this paper, we first characterize the Apéry set for a class of quotients of numerical semigroups. Under certain conditions, we then derive half-closed form formulas for their Frobenius number and genus. Furthermore, for specific values of part parameters, we obtain explicit formulas for the Frobenius number of certain quotients of numerical semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Frobenius problem for a class of quotients of numerical semigroups Liu, Feihu Combinatorics Given a numerical semigroup $S$ and a positive integer $p$, the quotient $\frac{S}{p}=\{x\in \mathbb{N} \mid px\in S\}$ also forms a numerical semigroup. In this paper, we first characterize the Apéry set for a class of quotients of numerical semigroups. Under certain conditions, we then derive half-closed form formulas for their Frobenius number and genus. Furthermore, for specific values of part parameters, we obtain explicit formulas for the Frobenius number of certain quotients of numerical semigroups. |
| title | The Frobenius problem for a class of quotients of numerical semigroups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.26415 |