A short proof that $w(3,k) \ge (1o(1))k^2$
Abstract
Here we present a short proof that the twocolor van der Waerden number $w(3,k)$ is bounded from below by $(1o(1))k^2$. Previous work has already shown that a superpolynomial lower bound holds for $w(3,k)$. However, we believe our result is still is of interest due to our techniques.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.07651
 arXiv:
 arXiv:2209.07651
 Bibcode:
 2022arXiv220907651H
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory
 EPrint:
 5 pages, comments welcome!