Sums of triples in Abelian groups

2023/01/04 by Feldman, Ido, Rinot, Assaf
#03E35 #05A17 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #Primary 03E02 #Secondary 03E75

paper · doi:10.48550/arxiv.2301.01671

Abstract

Motivated by a problem in additive Ramsey theory, we extend Todorcevic's partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for every Abelian group G of size ℵ₂, there exists a coloring c:G→\mathbb Z such that for every uncountable X⊆ G and every integer k, there are three distinct elements x,y,z of X such that c(x+y+z)=k.

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