The growth rate for three-colored sum-free sets
David Speyer
There seems to be a rule that all progress on the cap set problem should be announced on blogs, so let me continue the tradition. Robert Kleinberg, Will Sawin and I have found the rate of growth of three-colored sum-free subsets of , as . We just don’t know it is that what we’ve found!
The preprint is here.
Let me first explain the problem. Let be an abelian group. A subset of is said to be free of three term arithmetic progressions if there are no solutions to with , , , other than the trivial.