Abstract
A linear configuration is said to be common in an Abelian group 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 Jagger, Šťovíček and Thomason in graph theory, every configuration containing a 4-term arithmetic progression is uncommon. We prove this in Fpn for p≥5 and large n and in Zp for large primes p.
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