3 problems

Let $f_r(n,v,e)$ denote the maximum number of edges in an $r$-graph on $n$ vertices such that every set of $v$ vertices spans at most $e-1$ edges. For fixed integers $r>k\ge 2$ and…

Sparse hypergraph extremal-function conjecture. As $n\to\infty$,

A hypergraph is $c$-sparse if every vertex subset $S$ spans at most $c|S|^2$ edges. Let $(H)$ denote the independence number of a hypergraph $H$, and let $N$ be the number of verti…