Intersections of iterated shadows

Hou Tin Chau, David Ellis, Marius Tiba

We show that if $\mathcal{A}\subset \left(\genfrac{}{}{0ex}{}{[n]}{n/2}\right)$ with measure bounded away from zero and from one, then the $\Omega (\sqrt{n})$-iterated upper shadows of $\mathcal{A}$ and $\mathc…