A short proof that $w(3,k) \ge (1-o(1))k^2$
Abstract
Here we present a short proof that the two-color van der Waerden number $w(3,k)$ is bounded from below by $(1-o(1))k^2$. 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:
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arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- arXiv:
- arXiv:2209.07651
- Bibcode:
- 2022arXiv220907651H
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Number Theory
- E-Print:
- 5 pages, comments welcome!