MINIMAL UNIFORM COVERS ON FINITE SETS

摘要

In the power set lattice of a set with n < ∞ elements, a collection C of r element subsets is defined to be a uniform cover for the q ele¬ment subsets, q≥ r, if each q-set includes the same number A of r-sets from C. λ is called the weight of the cover. If no proper subset of C is a uniform cover, λis a minimal uniform cover. This extremal set problem is shown to subtend several well-known combinatorial systems:Steiner triples [27], Hanani quadruples [9], 5-designs [2], etc.