Numerical Sets, Core Partitions, and Integer Points in Polytopes
Combinatorics
2022-01-25 v1
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.
Cite
@article{arxiv.1509.06077,
title = {Numerical Sets, Core Partitions, and Integer Points in Polytopes},
author = {Hannah Constantin and Benjamin Houston-Edwards and Nathan Kaplan},
journal= {arXiv preprint arXiv:1509.06077},
year = {2022}
}
Comments
Submitted, 25 Pages