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Integer colorings with forbidden rainbow sums
For a set of positive integers , an -coloring of is
rainbow sum-free if it contains no rainbow Schur triple. In this paper we
initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of
sum-free sets, which asks for the subsets of with the maximum number of
rainbow sum-free -colorings. We show that for , the interval is
optimal, while for , the set is optimal. We
also prove a stability theorem for . The proofs rely on the hypergraph
container method, and some ad-hoc stability analysis.Comment: 20 page
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