Set systems with restricted -wise -intersections modulo a prime number

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• 作者：Jiuqiang Liu ; Wenbo Yang
• 刊名：European Journal of Combinatorics
• 出版年：February, 2014
• 年：2014
• 卷：36
• 期：Complete
• 页码：707-719
• 全文大小：402 K

文摘

The classical Erd枚s-Ko-Rado theorem on the size of an intersecting family of -subsets of the set is one of the most basic intersection theorems for set systems. Since the Erd枚s-Ko-Rado theorem was published, there have been many intersection theorems on set systems appeared in the literature, such as the well-known Frankl-Wilson theorem, Alon-Babai-Suzuki theorem, Grolmusz-Sudakov theorem, and Qian-Ray-Chaudhuri theorem. In this paper, we will survey results on intersecting families and derive extensions for these well-known intersection theorems to -wise -intersecting and cross-intersecting families by employing the existing linear algebra methods.