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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
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Abstract |
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A numerical semigroup is an additive subsemigroup of the nonnegative integers with finite complement, and the square-free divisor complex of an element is a simplicial complex 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. |
Keywords
nonunique factorization, numerical semigroup, square-free
divisor complex, simplicial complex
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Mathematical Subject Classification 2010
Primary: 13D02, 20M13, 20M14
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Milestones
Received: 1 May 2018
Revised: 17 August 2020
Accepted: 15 September 2020
Published: 4 March 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Jackson Autry | |
| Department of Mathematics San Diego State University San Diego, CA United States |
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| Paige Graves | |
| Department of Mathematics University of La Verne La Verne, CA United States |
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| Jessie Loucks | |
| Department of Mathematics Sacramento State University Sacramento, CA United States |
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| Christopher O’Neill | |
| Department of Mathematics and
Statistics San Diego State University San Diego, CA United States |
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| Vadim Ponomarenko | |
| Department of Mathematics and
Statistics San Diego State University San Diego, CA United States |
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| Samuel Yih | |
| Department of Mathematics Pomona College Claremont, CA United States |
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