4 problems

Asymptotic extremal conjecture for ordered 3-uniform tight paths. The constructions described in the source are asymptotically optimal:

Let $\mathcal{P}$ be a hereditary property of ordered hypergraphs. For every constant $c>0$, suppose there exists an $N=N(c)\in\mathbb{N}$ such that $|\mathcal{P}_N|>c^N$. The orde…

Let $F$ be an $r$-uniform forest with interval chromatic number $r$. Füredi–Jiang–Kostochka–Mubayi–Verstraëte conjecture. The maximum number of edges in a vertex-ordered $r$-unifor…

Pach–Tardos conjecture for ordered forests. Let $r\geq 2$. Then for any ordered $r$-uniform forest $F$ with interval chromatic number $r$,