论文标题
希尔顿 - 米勒定理的产品版本
A Product Version of the Hilton-Milner Theorem
论文作者
论文摘要
$ k $ \ {1,2，\ ldots，n \} $的两个家庭$ \ nathcal {f}，\ nathcal {g} $ of $ k $ -subsets of $ \ {1,2，\ ldots，n \} $，如果$ f \ cap g \ neq \ nequalyset for All $ f \ for All $ f \ in All \ in \ in \ f \ in \ f \ in \ f f \ cap g \ nequ}和$ \ cap \ {f \ colon f \ in \ mathcal {f} \} = \ emptySet = \ cap \ {g \ colon g \ in \ mathcal {g} \} $。在本文中，我们确定了$ \ {1,2，\ ldots，n \ ldots，n \} $ for $ n \ geq 4k $，$ k \ geq 8 $的两个非客气交叉交叉交流家庭的最大产品，这是古典希尔顿·米尔顿 - 吉尔顿 - 吉尔顿 - 吉尔顿 - geq 4K $，$ n \ geq 4k $，$ n \ geq $ s。
Two families $\mathcal{F},\mathcal{G}$ of $k$-subsets of $\{1,2,\ldots,n\}$ are called non-trivial cross-intersecting if $F\cap G\neq \emptyset$ for all $F\in \mathcal{F}, G\in \mathcal{G}$ and $\cap \{F\colon F\in \mathcal{F}\}=\emptyset=\cap \{G\colon G\in \mathcal{G}\}$. In the present paper, we determine the maximum product of the sizes of two non-trivial cross-intersecting families of $k$-subsets of $\{1,2,\ldots,n\}$ for $n\geq 4k$, $k\geq 8$, which is a product version of the classical Hilton-Milner Theorem.
