Cross -intersecting families on set systems

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• 作者：Jiuqiang Liu ; Xiaodong Liu
• 关键词：Erdő ; s– ; Ko– ; Rado theorem ; Frankl– ; Ray-Chaudhuri– ; Wilson theorems ; Frankl– ; Fü ; redi’ ; s conjecture ; Snevily’ ; s conjecture
• 刊名：Discrete Mathematics
• 出版年：2010
• 出版时间：28 February 2010
• 年：2010
• 卷：310
• 期：4
• 页码：720-726
• 全文大小：429 K

文摘

Let be a set of s positive integers. Suppose that and are two collections of subsets of [n]={1,2,…,n} such that whenever i≠j. If the set systems satisfy one of the following conditions:

(1) implies A_i=B_i

(2) A_i∩B_j≤A_j∩B_j with equality possible only when A_i∩B_i>A_j∩B_j for i≠j, then we bound m as This result extends Snevily’s theorem to cross -intersecting two families.