A product version of the Hilton-Milner-Frankl theorem  

作　　者：Peter Frankl Jian Wang 

机构地区：[1]Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences,Budapest H-1053,Hungary [2]Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China

出　　处：《Science China Mathematics》2024年第2期455-474,共20页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11701407)

摘　　要：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.

关 键 词：extremal set theory cross t-intersecting family product version non-trivial 

分 类 号：O157.5[理学—数学]