论文标题
联合关联集的渐近版本猜想
An asymptotic version of the union-closed sets conjecture
论文作者
论文摘要
我们表明，补充$ 2^{\ {\ {1,2，\ ldots，n \}}} \ setMinus a $ a $ closed家族的$ a \ subset 2^{\ subset 2^{\ subset 2^{\ subset 2^{\ c {1,2，\ ldots，n \} $ s $ sepminus在补充中最大的平均设置大小。通过相同的证据，我们在联合关闭家庭的补充中获得了平均频率的急剧上限。这意味着根据联合锁定家庭的补充而提出的联盟封闭式集的渐近版本。
We show that the biggest possible average set size in the complement $2^{\{1,2,\ldots, n\}} \setminus A$ of a union-closed family $A \subset 2^{\{1,2, \ldots, n\}}$ is $\tfrac{n+1}{2}$. With the same proof we get a sharp upper bound for the average frequency in complements of union-closed families. This implies an asymptotic version of the union-closed sets conjecture, formulated in terms of complements of union-closed families.
