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This web page contains the abstract of my paper:

"Some Results on Systems of Finite Sets that Satisfy a Certain Intersection Condition" with L.M.H. Ein, D.R. Richman, D.J. Kleitman and D. Sturtevant, Studies in Applied Mathematics, 65(1981), p. 269-274.

Abstract: Let S be a finite set, and fix K>2. Let F be a family of subsets of S with the property that whenever A1,...,AK are sets in F, not necessarily distinct, and intersection{A1,...,AK}=empty set, then union{A1,...,AK}=S. We prove here that the maximum size of such a family is 2**(|S|-1)+1. If we require that the sets A1,...,AK be distinct, then the maximum size of F is again 2**(|S|-1)+1, provided that |S|>=log2(K-2)+3.

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