Classifications of ℓ-Zero-Sumfree Sets

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 posets and the characteristic polynomials of the corresponding coordinate subspace arrangements.