Square-free divisor complexes of certain numerical semigroup elements

Abstract

A numerical semigroup $S$ is an additive subsemigroup of the nonnegative integers with finite complement, and the square-free divisor complex of an element $m\in S$ is a simplicial complex ${\mathrm{\Delta }}_m$ that arises in the study of multigraded Betti numbers. We compute square-free divisor complexes for certain classes numerical semigroups, and exhibit a new family of simplicial complexes that occur as the square-free divisor complex of some numerical semigroup element.