Given a dense subset A of the first n positive integers, we provide a short proof showing that for p = ω(n-2/3), the so-called randomly perturbed set A∩ [n]p a.a.s. has the property that any 2-coloring of it has a monochromatic Schur triple, i.e., a triple of the form (a, b, a + b). This result is optimal since there are dense sets A, for which A ∩ [n]p does not possess this property for p = o(n-2/3).
- Ramsey theory
- Random sets
- Schur triples
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