On integer partitions corresponding to numerical semigroups
Combinatorics
2023-02-17 v1 Group Theory
Number Theory
Abstract
Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. We explore this connection between partitions and numerical semigroups with a focus on classifying the partitions that appear in the image of the injection from numerical semigroups. In particular, we count the number of partitions that correspond to numerical semigroups in terms of genus, Frobenius number, and multiplicity, with some restrictions.
Cite
@article{arxiv.2302.08391,
title = {On integer partitions corresponding to numerical semigroups},
author = {Hannah E. Burson and Hayan Nam and Simone Sisneros-Thiry},
journal= {arXiv preprint arXiv:2302.08391},
year = {2023}
}