We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, in particular Arf and saturated numerical semigroups.
📌 3 Key Takeaways
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Objective & Hypothesis:A numerical semigroup is perfect if it does not have isolated gaps.
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Key Findings & Data:We also study the perfect monoid, which is a subset of $\N$ that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of $\N$.
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Conclusion & Impact:We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, in particular Arf and saturated numerical semigroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Arf semigroup · embedding dimension · Frobenius number
Abstract
A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfect numerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them. We also study the perfect monoid, which is a subset of $\N$ that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of $\N$. We give an algorithm to calculate it. We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, in particular Arf and saturated numerical semigroups.
FRÍAS, M. Á. M., ROSALES, J. C. (2019). Perfect numerical semigroups. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1742–1754. https://ajindex.com/articles/212739