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arXiv · 2211.07811

The Expected Embedding Dimension, type and weight of a Numerical Semigroup

Nathan Kaplan·Deepesh Singhal
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Abstract

We study statistical properties of numerical semigroups of genus $g$ as $g$ goes to infinity. More specifically, we answer a question of Eliahou by showing that as $g$ goes to infinity, the proportion of numerical semigroups of genus $g$ with embedding dimension close to $g/\sqrt{5}$ approaches $1$. We prove similar results for the type and weight of a numerical semigroup of genus $g$.

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Nathan Kaplan, Deepesh Singhal. 2022-11-15. The Expected Embedding Dimension, type and weight of a Numerical Semigroup. https://arxiv.org/abs/2211.07811

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