论文标题
枚举与数值半群相关的数值集
Enumerating numerical sets associated to a numerical semigroup
论文作者
论文摘要
数值集$ t $是包含$ 0 $且具有有限补充的$ \ mathbb n_0 $的子集。 $ t $的原子单体是\ Mathbb n_0 $的$ x \的集合，因此$ x+t \ t \ subseteq t $。 Marzuola和Miller引入了反原子问题：多少个数值集具有给定的原子单体？这相当于要求具有一组钩长的整数分区数量。我们介绍了数值半群$ s $的空隙，并表明带有原子MONOID $ S $的数值集在本poset的某些顺序中。当$ s $具有较小的类型时，我们使用此表征来回答抗原子问题。
A numerical set $T$ is a subset of $\mathbb N_0$ that contains $0$ and has finite complement. The atom monoid of $T$ is the set of $x \in \mathbb N_0$ such that $x+T \subseteq T$. Marzuola and Miller introduced the anti-atom problem: how many numerical sets have a given atom monoid? This is equivalent to asking for the number of integer partitions with a given set of hook lengths. We introduce the void poset of a numerical semigroup $S$ and show that numerical sets with atom monoid $S$ are in bijection with certain order ideals of this poset. We use this characterization to answer the anti-atom problem when $S$ has small type.
