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An application of Lovász' local lemma‐A new lower bound for the van der Waerden number

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

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 .

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