On the $\ell$-th largest degree of an intersecting family

Hao Huang, Rui Rao

Let $\mathcal{F}\subset \left(\genfrac{}{}{0ex}{}{[n]}{k}\right)$ be an intersecting family. For an element $i\in [n]$, the degree of $i$ is the number of sets in $\mathcal{F}$ that contain $i$. Assume that t…