Bounds on Van der Waerden Numbers and Some Related Functions

Tom Brown, Bruce M. Landman, Aaron Robertson

For positive integers $s$ and $k_1,k_2,...,k_s$, let $w(k_1,k_2,...,k_s)$ be the minimum integer $n$ such that any $s$-coloring $\{1,2,...,n\}\to \{1,2,...,s\}$ admits a $k_i$-…