On Some Tactical Configurations

Abstract

Given a set E of v elements, and given positive integers k, l (l ≤ k ≤ v), and λ, we understand by a tactical configurationC[k, l, λ, v] (briefly, configuration) a system of subsets of E, having k elements each, such that every subset of E having l elements is contained in exactly λ sets of the system.A necessary condition for the existence of a configuration C[k, l, λ, v] is known (6) to be