A short proof that w(3,k) ≥ (1-o(1))k²

2022/09/16 by Zach Hunter, Hunter, Zach
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2209.07651

openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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))k². 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.

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