  A numerical semigroup $S$ is an additive subsemigroup of the non-negative
integers with finite complement, and the squarefree divisor complex of an
element $m \in S$ is a simplicial complex $\Delta_m$ that arises in the study
of multigraded Betti numbers. We compute squarefree divisor complexes for
certain classes numerical semigroups, and exhibit a new family of simplicial
complexes that are occur as the squarefree divisor complex of some numerical
semigroup element.
