Octopuses in the Boolean cube: families with pairwise small intersections, part I

Andrey Kupavskii, Fedor Noskov

Let ${\mathcal{F}}_1,\dots ,{\mathcal{F}}_{\ell }$ be families of subsets of $\{1,\dots ,n\}$. Suppose that for distinct $k,k^{\prime }$ and arbitrary $F_1 \in \mathcal F_{k}, F_2 \in \mathcal…