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arXiv · 2409.06376

A computational approach to the study of finite-complement submonids of an affine cone

J. C. Rosales·R. Tapia-Ramos·A. Vigneron-Tenorio
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Abstract

Let $\mathcal{C}\subseteq \mathbb{N}^p$ be an integer cone. A $\mathcal{C}$-semigroup $S\subseteq \mathcal{C}$ is an affine semigroup such that the set $\mathcal{C}\setminus S$ is finite. Such $\mathcal{C}$-semigroups are central to our study. We develop new algorithms for computing $\mathcal{C}$-semigroups with specified invariants, including genus, Frobenius element, and their combinations, among other invariants. To achieve this, we introduce a new class of $\mathcal{C}$-semigroups, termed $\mathcal{B}$-semigroups. By fixing the degree lexicographic order, we also research the embedding dimension for both ordinary and mult-embedded $\mathbb{N}^2$-semigroups. These results are applied to test some generalizations of Wilf's conjecture.

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J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio. 2024-09-10. A computational approach to the study of finite-complement submonids of an affine cone. https://arxiv.org/abs/2409.06376

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