子集系K分划定理的简短证明

A Short Proof for K-Partition Theorem of Family of Subsets

给出 Katona-Kleitman定理的推广定理的简短证明 .

The present paper presents a brief proof of the generalized Katona Kleitman theorem: Let S={1,2,…,n}, S 1,S 2,…,S k be the k partition of S and F be a family of the subsets of S , if there are no A,B in F, there must exist S 1 satisfying A∩S i=B∩S i, but for others S j(1≤j≠i≤k) A∩S jB∩S j , then |F|≤n [n/2].