  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.
