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A threshold property for intersections in a finite set
Authors:Jean-Luc Paillet
Institution:Université de Provence, 3 Place Victor Hugo, 13331 Marseille Cedex 3, France
Abstract:Let F be any family of subsets of a finite set E and let n be an integer, n<|F|. Under what condition does the knowledge of cardinals of m-intersections in F, for all mn, univocally determine the cardinal of any intersection in F, and what is the minimal condition? We give a complete answer to that. For any n, this determination property is satisfied by n if and only if |E|<2n, without further condition on F.
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