Note: On the asymptotic minimum number of monochromatic 3-term arithmetic progressions

  • Authors:

  • Pablo A. Parrilo;Aaron Robertson;Dan Saracino

  • Affiliations:

  • Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;Department of Mathematics, Colgate University, Hamilton, NY 13346, USA;Department of Mathematics, Colgate University, Hamilton, NY 13346, USA

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2008

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Abstract

Let V(n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1,2,...,n}. We show that167532768n^2(1+o(1))=