DISJOINT SYSTEMS

A disjoint system of type (for-all, there-is, k,n) is a collection C = {A1,...,A(m)} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair A(i) and A(j) of distinct members of C and for every A is-an-element-of A(i) there exists a B is-an-element-of A(j) that does not interesect A. Let D(n)(for-all, there-is, k) denote the maximum possible cardinality of a disjoint system of type (for-all, there-is, k,n). It is shown that for every fixed k greater-than-or-equal-to 2, [GRAPHICS] This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well. (C) 1995 John Wiley & Sons, Inc.