Strong qualitative independence

The subsets A, B of the n-element X are said to be s-strongly separating if the two sets divide X into four sets of size at least s. The maximum number h(n,s) of pairwise s-strongly separating subsets was asymptotically determined by Frankl (Ars Combin. 1 (1976) 53) for fixed s and large n. A new proof is given. Also, estimates for h(n, en) are found where c is a small constant. (C) 2003 Elsevier B.V. All rights reserved.