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- W4377818744 abstract "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 Erdős-Rothschild 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." @default.
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- W4377818744 date "2023-10-01" @default.
- W4377818744 modified "2023-10-11" @default.
- W4377818744 title "Integer colorings with forbidden rainbow sums" @default.
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- W4377818744 doi "https://doi.org/10.1016/j.jcta.2023.105769" @default.
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