论文标题
希尔顿 - 米尔纳 - 弗朗克定理的产品版本
A Product Version of the Hilton-Milner-Frankl Theorem
论文作者
论文摘要
$ k $ \ {1,2，\ ldots，n \} $的两个家庭$ \ Mathcal {f}，\ Mathcal {g} $ of $ k $ -subsets of $ \ {1,2，\ ldots，n \} $，如果$ | f \ cap g | \ cap g | \ cap g | \ cap g | f | \ Mathcal {g} $和$ | \ cap \ {f \ colon f \ in \ Mathcal {f} \} | <t $，$ | \ cap \ cap \ {g \ colon g \ in \ Mathcal {g}在本文中，我们确定了$ \ {1,2，\ ldots，n \ ldots，n \ geq 4（t+2）^2k^2 $，$ k \ egeq 5 $，这是一个产品版本，这是$ n \ geq 4（t+2）^2k^2 $ for $ n \ geq 4（t+2）^2k^2 $，是$ n \ geq 4（t+2）^2k^2 $，是$ n \ geq 4（t+2），是$ n \ geq 4（t+2），是$ n \ geq 4（t+2），这是一个产品版本，
Two families $\mathcal{F},\mathcal{G}$ of $k$-subsets of $\{1,2,\ldots,n\}$ are called non-trivial cross $t$-intersecting if $|F\cap G|\geq t$ for all $F\in \mathcal{F}, G\in \mathcal{G}$ and $|\cap \{F\colon F\in \mathcal{F}\}|<t$, $|\cap \{G\colon G\in\mathcal{G}\}|<t$. In the present paper, we determine the maximum product of the sizes of two non-trivial cross $t$-intersecting families of $k$-subsets of $\{1,2,\ldots,n\}$ for $n\geq 4(t+2)^2k^2$, $k\geq 5$, which is a product version of the Hilton-Milner-Frankl Theorem.
