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arXiv · 2407.18984

Semi-covariety of numerical semigroups

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

The main aim of this work is to introduce and justify the study of semi-covarities. A {\it semi-covariety} is a non-empty family $\mathcal{F}$ of numerical semigroups such that it is closed under finite intersections, has a minimum, $\min(\mathcal{F}),$ and if $S\in \mathcal{F}$ being $S\neq \min(\mathcal{F})$, then there is $x\in S$ such that $S\backslash \{x\}\in \mathcal{F}$. As examples, we will study the semi-covariety formed by all the numerical semigroups containing a fixed numerical semigroup, and the semi-covariety composed by all the numerical semigroups of coated odd elements and fixed Frobenius number.

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M. A. Moreno-Frías, J. C. Rosales. 2024-07-24. Semi-covariety of numerical semigroups. https://arxiv.org/abs/2407.18984

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