Classifications of ℓ-Zero-Sumfree Sets

2019/04/18 by Adams, Ashleigh, Hall, Carole, Stucky, Eric
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1904.08989

Abstract

The set of all ℓ-zero-sumfree subsets of ℤ/nℤ is a simplicial complex denoted by Δ_n,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 Δ_n,ℓ for several infinite families of parameters, and compute the intersection lattices and the characteristic polynomials of the corresponding coordinate subspace arrangements.

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