35 research outputs found
A lower bound for the -multicolored sum-free problem in
In this paper, we give a lower bound for the maximum size of a -colored
sum-free set in , where and are fixed and
tends to infinity. If is a prime power, this lower bound matches (up to
lower order terms) the previously known upper bound for the maximum size of a
-colored sum-free set in . This generalizes a result of
Kleinberg-Sawin-Speyer for the case and as part of our proof we also
generalize a result by Pebody that was used in the work of
Kleinberg-Sawin-Speyer. Both of these generalizations require several key new
ideas