2 problems

Let $m(n,k,s)$ denote the maximum size of a $k$-uniform hypergraph on an $n$-element vertex set whose covering number is $s$. For $s\geq 3$, $k>k_0(s)$, and $n\geq n_0(k,s)$, the a…

For integers $0\le a<b\le k$, let … where the maximum is over intersecting families ${\mathcal F}\subset {[n]\choose k}$ with covering number $\tau({\mathcal F})=b$. In particular,…