Classifications of ℓ-Zero-Sumfree Sets
Keywords: additive combinatorics, sumfree sets, zero-sumfree sets, simplicial complex, subspace arrangements, characteristic polynomial, h-vector, f-vector, unimodal
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.
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. Retrieved from https://journals.calstate.edu/pump/article/view/1805
Copyright (c) 2019 Ashleigh Adams, Carole Hall, Eric Stucky
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