2 problems

Let $R_3(n;3,2)$ be the least integer $N$ such that every three-coloring of the edges of the complete three-uniform hypergraph $K_N^{(3)}$ contains a copy of $K_n^{(3)}$ using at m…

For positive integers $n\geq k$ and $r>s$, let $A_k(n;r,s)$ be the least $N$ such that every $r$-coloring of $[N]^{(k)}$ contains a tight monotone path on $n$ edges using at most…