On a limit theorem in combinatorical analysis

Abstract

Given a set E of n elements and given positive integers k, 1, (Es ks n), we understand by M(k, I, n) a minimal system of k-tuples (subsets of E having k elements each) such that every I-tuple is contained in at least one k-tuple of the system. Similarly we denote by m(k, I, n) a maximal system of k-tuples such that every I-tuple is contained in at most one set of the system. The number of k-tuples in these systems will be denoted by M(k, I, n) and Z(k. I. 71) respectively. Further we denote

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