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

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 S is a simplicial complex Δm 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.

nonunique factorization, numerical semigroup, square-free divisor complex, simplicial complex
Mathematical Subject Classification 2010
Primary: 13D02, 20M13, 20M14
Received: 1 May 2018
Revised: 17 August 2020
Accepted: 15 September 2020
Published: 4 March 2021

Communicated by Kenneth S. Berenhaut
Jackson Autry
Department of Mathematics
San Diego State University
San Diego, CA
United States
Paige Graves
Department of Mathematics
University of La Verne
La Verne, CA
United States
Jessie Loucks
Department of Mathematics
Sacramento State University
Sacramento, CA
United States
Christopher O’Neill
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States
Samuel Yih
Department of Mathematics
Pomona College
Claremont, CA
United States