论文标题
数值半群，多面体和POSETS III：最小的表现和面尺寸
Numerical semigroups, polyhedra, and posets III: minimal presentations and face dimension
论文作者
论文摘要
本文是一系列手稿中的第三篇，它们检查了Kunz Polyhedron $ p_m $的组合，其正整数点与数值半群（Cofinite subigroups（$ \ Mathbb z _ {\ ge 0}）的数值subsemigroups（Cofinite subsemigroups），其最小的正元素是$ m $ $ m $。 $ p_m $的面孔是由一个有限的posets（称为kunz posets）索引的，这些家族是从位于给定脸上的数值半群的划分中获得的。在本文中，我们表征了数值半群的最小呈现的程度可以从其Kunz Poset中回收。在这样做的过程中，我们证明了所有位于给定面孔$ p_m $的内部内部的数值半群具有相同的最小呈现基础性，并且我们提供了一种组合方法，可以从其相应的kunz poset中获得面部尺寸的组合方法。
This paper is the third in a series of manuscripts that examine the combinatorics of the Kunz polyhedron $P_m$, whose positive integer points are in bijection with numerical semigroups (cofinite subsemigroups of $\mathbb Z_{\ge 0}$) whose smallest positive element is $m$. The faces of $P_m$ are indexed by a family of finite posets (called Kunz posets) obtained from the divisibility posets of the numerical semigroups lying on a given face. In this paper, we characterize to what extent the minimal presentation of a numerical semigroup can be recovered from its Kunz poset. In doing so, we prove that all numerical semigroups lying on the interior of a given face of $P_m$ have identical minimal presentation cardinality, and we provide a combinatorial method of obtaining the dimension of a face from its corresponding Kunz poset.
