论文标题
改进了弗兰克尔联盟锁定的猜想的下限
Improved Lower Bound for Frankl's Union-Closed Sets Conjecture
论文作者
论文摘要
我们验证了吉尔默（Gilmer）最近提出的明确不平等，因此证明，对于任何非公开的联盟封闭的家庭$ f \ subseteq 2^{[n]} $，在[n] $中包含一些$ i \ in [n] $，至少在$ \ frac {3- \ frac {3- \ \ sqrt {5}}} $ 0.38 $ 0.38中。通过计算机计算检查一种情况，即明确的单变量不等式。
We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty union-closed family $F \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $F$. One case, an explicit one-variable inequality, is checked by computer calculation.
