Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903630 | European Journal of Combinatorics | 2018 | 6 Pages |
Abstract
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 pâ¤k then w(r,k)>pâ
wrârp,kâ1. This recurrence gives the lower bound w(r,p+1)>prâ12p when râ¤p, which generalizes Berlekamp's theorem on 2-colorings, and gives the best known bound for a large interval of r. The recurrence can also be used to construct explicit valid colorings, and it improves known lower bounds on small van der Waerden numbers.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Thomas Blankenship, Jay Cummings, Vladislav Taranchuk,