For a set of positive integers A⊆[n], an r-coloring of A 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 [n] with the maximum number of
rainbow sum-free r-colorings. We show that for r=3, the interval [n] is
optimal, while for r≥8, the set [⌊n/2⌋,n] is optimal. We
also prove a stability theorem for r≥4. The proofs rely on the hypergraph
container method, and some ad-hoc stability analysis.Comment: 20 page