Classifications of ℓ-Zero-Sumfree Sets - Adams, Ashleigh; Hall, Carole; Stucky, Eric (The PUMP Journal of Undergraduate Research, 2019)
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.