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