Numerical Sets, Core Partitions, and Integer Points in Polytopes [article]

Hannah Constantin, Benjamin Houston-Edwards, Nathan Kaplan
<span title="2015-09-21">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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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