A New Lower Bound for van der Waerden Numbers

Thomas Blankenship, Jay Cummings, Vladislav Taranchuk

In this paper we prove a new recurrence relation on the van der Waerden numbers, $w(r,k)$. In particular, if $p$ is a prime and $p\le k$ then $w(r, k) > p \cdot \left(w\left(r - \…