论文标题
关于数值半群的最低介绍的基数
On the cardinality of minimal presentations of numerical semigroups
论文作者
论文摘要
在本文中，我们考虑了以下问题：“鉴于数值半群$ s $的多重性$ m $和嵌入尺寸$ e $，关于最小$ s $的最低介绍的基数$η$可以说什么？”我们利用了最近引入的kunz nilsemigroup的概念来从组合（POSET理论）的角度解决这个问题。除了以显式结构和一般界限的形式对此问题提出重大进展，我们还为Kunz Nilsemigroups提供了独立的介绍，避免了其许多原始材料所必需的多面体几何形状。
In this paper, we consider the following question: "given the multiplicity $m$ and embedding dimension $e$ of a numerical semigroup $S$, what can be said about the cardinality $η$ of a minimal presentation of $S$?" We approach this question from a combinatorial (poset-theoretic) perspective, utilizing the recently-introduced notion of a Kunz nilsemigroup. In addition to making significant headway on this question beyond what was previously known, in the form of both explicit constructions and general bounds, we provide a self-contained introduction to Kunz nilsemigroups that avoids the polyhedral geometry necessary for much of their source material.
