Linear configurations containing 4-term arithmetic progressions are uncommon

2021/06/12 by Versteegen, Leo
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.06846

Abstract

A linear configuration is said to be common in G if every 2-coloring of G yields at least the number of monochromatic instances of a randomly chosen coloring. Saad and Wolf asked whether, analogously to a result by Thomason in graph theory, every configuration containing a 4-term arithmetic progression is uncommon. We prove this in \mathbbF_pⁿ for p≥ 5 and large n and in ℤ_p for large primes p.

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