A 2-coloring of [1,n] can have (n2)/22 + O(n) monochromatic Schur triples, but not less!
Abstract
We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1,n] can have is (n2)/22 + O(n). This was solved independently by Tomasz Schoen.
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