首页|A product version of the Hilton-Milner-Frankl theorem
A product version of the Hilton-Milner-Frankl theorem
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Two families F and G of k-subsets of {1,2,...,n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F,G ∈ G and | ∩ {F:F ∈ F}|＜t,| ∩ {G:G ∈ G}|＜t.In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1,2,...,n} for n ≥ 4(t+2)2k2,k ≥ 5,which is a product version of the Hilton-Milner-Frankl theorem.
extremal set theorycross t-intersecting familyproduct versionnon-trivial
Peter Frankl、Jian Wang
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Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences,Budapest H-1053,Hungary
Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China
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