The multiples of a numerical semigroup

Ignacio Ojeda; José Carlos Rosales

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arXiv · 2402.04413

The multiples of a numerical semigroup

Ignacio Ojeda·José Carlos Rosales

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Abstract

Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension $e$ without any quotient of embedding dimension less than $e$, and provide new families with this property.

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Ignacio Ojeda, José Carlos Rosales. 2024-02-06. The multiples of a numerical semigroup. https://arxiv.org/abs/2402.04413

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