Families of finite sets satisfying an intersection condition
Families of finite sets satisfying an intersection condition
复制标题
满足交集条件的有限集族
DOI：
10.1017/s0004972700036777
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发表时间：
1976
影响因子：
0.7
通讯作者：
P. Frankl
中科院分区：
文献类型：
--
作者：
P. Frankl
证明了下面的定理。设X是基数n≥2的有限集，F是X的子集族.假设对F1，F2，F3∈F有|F1∩F2∩F3|≥2.则|F|≤2n−2具有相等保持当且仅当对X的两个不同元素x，y，F={F⊆X|x∈F，y∈F}.
The following theorem is proved. Let X be a finite set of cardinality n ≥ 2, and let F be a family of subsets of X. Suppose that for F1, F2, F3 ∈ F we have |F1 ∩ F2 ∩ F3| ≥ 2. Then |F| ≤ 2n−2with equality holding if and only if for two different elements x, y of X, F = {F ⊆ X | x ∈ F, y ∈ F}.