3 problems

Let $k$ and $t$ be fixed, and let $D=\binom{k}{t}-1$. Consider a covering produced by the random greedy algorithm, and define its density as the number of blocks divided by the asy…

Let $1<\ell<k$ be fixed, and let $\mathcal H_{\ell,k}$ be the hypergraph on vertex set $\binom{[n]}{\ell}$ whose edges are the sets $\binom{A}{\ell}$ for $A\in\binom{[n]}{k}$. Let…

Let $k$ be a positive integer, and apply the simple random greedy algorithm to find a maximal collection of $k$-tuples with pairwise intersections of size at most $k-2$. The uncove…