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

Pablo A. Parrilo, Aaron Robertson, Dan Saracino

Let V(n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1,2,...,n}. We show that (1675/32768) n^2 (1+o(1)) <= V(n) <= (117/2192) n^2(1+…