EKR sets for large $n$ and $r$

Benjamin Bond

Let $\A\subset\binom{[n]}{r}$ be a compressed, intersecting family and let $X\subset [n]$. Let $\A(X)={A\in\A:A\cap X\ne\emptyset}$ and ${\S }_{n,r}=\left(\genfrac{}{}{0ex}{}{[n]}{r}\right)(1)$. Motivated by t…