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Numerical Sets, Core Partitions, and Integer Points in Polytopes
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<span title="2015-09-21">2015</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
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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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