Classifications of ℓ-Zero-Sumfree Sets

  • Ashleigh Adams University of Minnesota – Twin Cities
  • Carole Hall University of Minnesota – Twin Cities
  • Eric Stucky University of Minnesota – Twin Cities
DOI: https://doi.org/10.46787/pump.v2i0.1805
Keywords: additive combinatorics, sumfree sets, zero-sumfree sets, simplicial complex, subspace arrangements, characteristic polynomial, h-vector, f-vector, unimodal

Abstract

The set of all ℓ-zero-sumfree subsets of ℤ/nℤ is a simplicial complex denoted by Δn, ℓ. We create an algorithm via defining a set of integer partitions we call (n,ℓ)-congruent partitions in order to compute this complex for moderately-sized parameters n and ℓ. We also theoretically determine Δn, ℓ for several infinite families of parameters, and compute the intersection posets and the characteristic polynomials of the corresponding coordinate subspace arrangements.

 

Author Biographies

Ashleigh Adams, University of Minnesota – Twin Cities

Department of Mathematics,

Undergraduate Student

Carole Hall, University of Minnesota – Twin Cities

Department of Mathematics,

Undergraduate Student

Eric Stucky, University of Minnesota – Twin Cities

Department of Mathematics,

Graduate Student

Published
2019-09-17
How to Cite
Adams, A., Hall, C., & Stucky, E. (2019). Classifications of ℓ-Zero-Sumfree Sets. The PUMP Journal of Undergraduate Research, 2, 179-198. https://doi.org/10.46787/pump.v2i0.1805
Issue
Vol. 2 (2019): PUMP Journal of Undergraduate Research
Section
Articles

Copyright (c) 2019 Ashleigh Adams, Carole Hall, Eric Stucky

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