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arXiv · 2506.17152

Affine semigroups without consecutive small elements

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

An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all $\mathcal{A}$-semigroups with a given Frobenius element (denoted by $\mathcal{A}(f)$), and with fixed Frobenius element and multiplicity. Moreover, we analyze the $\mathcal{A}(f)$-systems of generators. Furthermore, we study $\mathcal{A}$-numerical semigroups with maximal embedding dimension, fixed Frobenius number and multiplicity, providing an algorithm for their computation and a graphical classification.

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J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio. 2025-06-20. Affine semigroups without consecutive small elements. https://arxiv.org/abs/2506.17152

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