On strengthenings of the intersecting shadow theorem

P. Frankl, G. O. H. Katona

Let $n>k>t\ge j\ge 1$ be integers. Let $X$ be an $n$-element set, $\left(\genfrac{}{}{0ex}{}{X}{k}\right)$ the collection of its $k$-subsets. A family $\mathcal{F}\subset \left(\genfrac{}{}{0ex}{}{X}{k}\right)$ is called $t$…