Resistant sets in the unit hypercube

Ideal matrices and clutters are prevalent in Combinatorial Optimization, ranging from balanced matrices, clutters of T-joins, to clutters of rooted arborescences. Most of the known examples of ideal clutters are combinatorial in nature. In this paper, rendered by the recently developed theory of cuboids, we provide a different class of ideal clutters, one that is geometric in nature. The advantage of this new class of ideal clutters is that it allows for infinitely many ideal minimally non-packing clutters. We characterize the densest ideal minimally non-packing clutters of the class. Using the tools developed, we then verify the Replication Conjecture for the class.