4 problems

Let $K^{<(k)}_n$ denote the ordered complete $k$-uniform hypergraph, let $MP^{<(k)}_{k+1}$ denote the monotone $(k+1)$-vertex path in the $k$-uniform setting, and let $t_{k-1}$ be…

Gir27ao–Janzer–Janzer conjecture. The ordered Ramsey number of $P^<_{k,n}$ in $q$ colors admits the displayed bound with an exponent linear in $q$.

Rohatgi's conjecture. The stated subquadratic bound holds for almost every ordered matching of each fixed interval chromatic number.

For integers $2\le k < s < n$ and $2\le t\le {s\choose k}$, let $r_k(s,t;P_n)$ be the minimum $N$ such that every red/blue coloring of the $k$-sets of $[N]$ contains a monochromati…