Squarefree divisor complexes of certain numerical semigroup elements

TL;DR

This paper studies the structure of squarefree divisor complexes associated with elements of numerical semigroups, providing explicit computations for specific classes and introducing a new family of such complexes.

Contribution

It computes squarefree divisor complexes for certain numerical semigroups and introduces a new family of complexes arising from these semigroups.

Findings

Explicit computation of complexes for specific classes

Introduction of a new family of simplicial complexes

Connections to multigraded Betti numbers

Abstract

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.