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arXiv · 1509.06077

Numerical Sets, Core Partitions, and Integer Points in Polytopes

Hannah Constantin·Benjamin Houston-Edwards·Nathan Kaplan
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Abstract

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.

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Hannah Constantin, Benjamin Houston-Edwards, Nathan Kaplan. 2015-09-21. Numerical Sets, Core Partitions, and Integer Points in Polytopes. https://doi.org/10.1007/978-3-319-68032-3_7

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