论文标题
非平凡的3明相交家族的最大程度
The maximum measure of non-trivial 3-wise intersecting families
论文作者
论文摘要
令$ \ Mathcal g $为$ n $ element套件的子集。如果$ \ \ \ \ \ natcal g $在$ \ Mathcal g $中的任何三个子集的交集是非空的，但是所有子集的交集是空的，则家族$ \ Mathcal G $称为非平地$ 3 $相交的相交。对于（0,1）$中的实际数字$ p \，我们以$ p^{| g |}（1-p）^{n- | g |} $的总和来定义家庭的度量。我们确定非平凡的$ 3 $相交家庭的最大度量。我们还讨论了相应的最佳结构的独特性和稳定性。这些结果是通过解决线性编程问题获得的。
Let $\mathcal G$ be a family of subsets of an $n$-element set. The family $\mathcal G$ is called non-trivial $3$-wise intersecting if the intersection of any three subsets in $\mathcal G$ is non-empty, but the intersection of all subsets is empty. For a real number $p\in(0,1)$ we define the measure of the family by the sum of $p^{|G|}(1-p)^{n-|G|}$ over all $G\in\mathcal G$. We determine the maximum measure of non-trivial $3$-wise intersecting families. We also discuss the uniqueness and stability of the corresponding optimal structure. These results are obtained by solving linear programming problems.
