Numerical semigroups with quasi maximal embedding dimension

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-23 DOI:10.1007/s11587-024-00872-7

D. Llena, J. C. Rosales

引用次数: 0

Abstract

Consider \(x\in {\mathbb {N}}\setminus \{0\}\). A QMED(x)-semigroup is a numerical semigroup S such that \(S{\setminus }\{0\}=\{a+kx \mid a\in {\text {msg}}(S) \text{ and } k\in {\mathbb {N}}\}\) where \({\text {msg}}(S)\) denotes the minimal system of generators of S. Note that if x is the multiplicity of S then S is a maximal embedding dimension numerical semigroup. In this work, we show that the set of all QMED(x)-semigroups is a Frobenius pseudo-variety giving the associated tree. Furthermore, we give formulas to obtain the Frobenius number, type, and genus of this class of semigroups.

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具有准最大嵌入维数的数值半群

考虑 \(x\in {\mathbb {N}}\setminus\{0\}\).一个 QMED(x)-semigroup 是一个数值半群 S，使得 \(S{setminus }\{0\}=\{a+kx \mid a\in {\text {msg}}(S) \text{ and } k\in {\mathbb {N}}\}) 其中 \({\text {msg}}(S)\) 表示 S 的最小子系统。请注意，如果 x 是 S 的乘数，那么 S 就是一个最大嵌入维数半群。在这项工作中，我们证明了所有 QMED(x)-semigroups 的集合是一个给出相关树的 Frobenius 伪变体。此外，我们还给出了这一类半群的弗罗贝尼斯数、类型和属的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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