Three-color van der Waerden numbers grow super-exponentially

The van der Waerden number w(k;r) is the minimum positive integer N such that every r-coloring of the positive integers up to N contains a monochromatic k-term arithmetic progression. Estimating these numbers has remained a challenging open problem for the past century. In this talk, we will sketch a proof that the three-color van der Waerden number w(k;3) grows faster than any exponential in k. This settles several longstanding conjectures in the area. Time permitting, we will discuss a variety of related results. Based on joint work with Zach Hunter.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/