Numerical Sets, Core Partitions, and Integer Points in Polytopes

Hannah Constantin, Benjamin Houston-Edwards, Nathan Kaplan

Published 2015-09-21Version 1

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.