Numerical Sets, Core Partitions, and Integer Points in Polytopes
Numerical Sets, Core Partitions, and Integer Points in Polytopes
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多面体中的数值集、核心划分和整数点
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Kaplan
中科院分区：
文献类型：
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作者：
Hannah Constantin;Benjamin Houston;N. Kaplan
我们研究了数值集和整数分区之间的对应关系，从而导致同时核心分区和某个多面体的整数点之间的双射。我们使用这种对应证明组合结果的核心分区。对于小的a值，我们给出了数值半群对应的（a，B）-核划分数的公式。我们还研究了给定钩子集的划分数。
We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results about core partitions. For small values of a, we give formulas for the number of (a, b)-core partitions corresponding to numerical semigroups. We also study the number of partitions with a given hook set.