Phd Student finds value for van der Waerden number
Michal Kouril, working with Dr. Jerry Paul, computed the value of the van der Waerden number W(2,6).
A breakthrough has recently been made by Michal Kouril (recent Ph.D. student of Jerry Paul) in the computation of van der Waerden numbers W(K,L). Given positive integers K and L, the van der Waerden number W(K,L) is smallest integer n = W(K,L) such that whenever {1,2,...,n} is arbitrarily partitioned into K disjoint sets, at least one of the sets contains an arithmetic progression of length K. Ever since van der Waerden proved these numbers exist in the 1920s, there has been a great deal of interest in the combinatorics community in computing their actual values. In addition to other results on these numbers, Michal showed that W(2,6) = 1132, using clever heuristics to bound the search. He carried out the massive computation on the Beowulf clusters in the LINC lab, and, in the last stages, FPGAs to speed up the search. The last number W(2,L) to be computed (W(2,5) = 178) took place almost 30 years ago.