A 2-coloring of [1,n] can have (n²)/22 + O(n) monochromatic Schur triples, but not less!

1998/03/31 by Aaron Robertson, Doron Zeilberger
Mathematics · #math.CO #math.LO #msc:05D10 #msc:05A16

paper · pdf

published as Electronic Journal of Combinatorics 5 (1998), R19 · 4 pages, minor and subtle gap fixed, typos fixed

arxiv created 1998/08/12 · arxiv updated 2009/11/30

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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