1990/09/01 by Zoltán Szabó · 1 citation
Mathematics · Engineering · Computer Science · #Limits and Structures in Graph Theory #graph theory and CDMA systems #Coding theory and cryptography #Van der Waerden's theorem #Combinatorics #Integer (computer science) #Lemma (botany) #Mathematics #Upper and lower bounds #Arithmetic progression #Discrete mathematics #Computer science #Biology #Mathematical analysis
paper · doi:10.1002/rsa.3240010307
openalex publication_date 1990/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Abstract The van der Waerden number W(n) is the smallest integer so that if we divide the integers 1,2, …, W(n) into two classes, then at least one of them contains an arithmetic progression of length n . We prove in this paper that W(n) ≥ 2 n / n ϵ for all sufficiently large n .