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arXiv · 2305.02070

The ratio-covariety of numerical semigroups with fixed multiplicity and Frobenius number

M. A. Moreno-Frías·J. C. Rosales
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Abstract

In this work we will introduce the concept of ratio-covariety, as a nonempty family $\mathscr{R}$ of numerical semigroups verifying certain properties. This concept will allow us to: \begin{enumerate} \item Describe an algorithmic process to compute $\mathscr{R}.$ \item Prove the existence of the smallest element of $\sR$ that contains a set of positive integers. \item Talk about the smallest ratio-covariety that contains a finite set of numerical semigroups. \end{enumerate} In addition, in this paper we will apply the previous results to the study of the ratio-covariety $\mathscr{R}(F,m)=\{S\mid S \mbox{ is a numerical semigroup with Fro-} \mbox {benius number }F \mbox{ and multiplicity }m\}.$

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M. A. Moreno-Frías, J. C. Rosales. 2023-05-03. The ratio-covariety of numerical semigroups with fixed multiplicity and Frobenius number. https://arxiv.org/abs/2305.02070

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