The maximum sum of the sizes of all intersections within $m$-size families

Sumin Huang, Gyula O. H. Katona, Erfei Yue

For a family of sets $\mathcal{F}$, let $\ddot{I}‰(\mathcal{F}):={\sum }_{\{A,B\}\subset \mathcal{F}}|A\cap B|$. In this paper, we prove that provided $n$ is sufficiently large, for any $\ma…