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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.26415 |
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Table of 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.