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A 2-coloring of [1,n] can have (n^2)/22 + O(n) monochromatic Schur triples, but not less!

Aaron Robertson·Doron Zeilberger
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Abstract

We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1,n] can have is (n^2)/22 + O(n). This was solved independently by Tomasz Schoen.

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Aaron Robertson, Doron Zeilberger. 1998-08-12. A 2-coloring of [1,n] can have (n^2)/22 + O(n) monochromatic Schur triples, but not less!. https://arxiv.org/abs/math/9803149

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