不相容相交属性
Incompatible intersection properties
摘要：
设$\mathcal F\subset 2^{[n]}$是一个族，其中任意三个集合有非空交集，任意两个集合至少有$38$公共元素。证明了近似最佳可能界$|\mathcal F|\le 2^{n-2}$。我们相信$38$可以被$3$取代，并提供了一个简单的猜想，将暗示这一点。
英文摘要：
Let $\mathcal F\subset 2^{[n]}$ be a family in which any three sets have non-empty intersection and any two sets have at least $38$ elements in common. The nearly best possible bound $|\mathcal F|\le 2^{n-2}$ is proved. We believe that $38$ can be replaced by $3$ and provide a simple-looking conjecture that would imply this.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
