互补数值集
Complementary Numerical Sets
摘要：
数值集$S$是$\mathbb{N}$的余有限子集，它包含$0$。利用数值集和Young图之间的自然双射定义了一个数值集$\widetilde{S}$，使得它们的Young图是补图.我们确定各种性质的$\widetilde{S}$，特别是与眼睛关闭下添加（$S$和$\widetilde{S}$），这促进了一个数值集成为一个数值半群。
英文摘要：
A numerical set $S$ is a cofinite subset of $\mathbb{N}$ which contains $0$. We use the natural bijection between numerical sets and Young diagrams to define a numerical set $\widetilde{S}$, such that their Young diagrams are complements. We determine various properties of $\widetilde{S}$, particularly with an eye to closure under addition (for both $S$ and $\widetilde{S}$), which promotes a numerical set to become a numerical semigroup.
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