Vol. 14, No. 1, 2021

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Square-free divisor complexes of certain numerical semigroup elements

Jackson Autry, Paige Graves, Jessie Loucks, Christopher O’Neill, Vadim Ponomarenko and Samuel Yih

Vol. 14 (2021), No. 1, 1–9
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 ${\Delta }_{m}$ 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.

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Keywords
nonunique factorization, numerical semigroup, square-free divisor complex, simplicial complex
Mathematical Subject Classification 2010
Primary: 13D02, 20M13, 20M14