A 2-coloring of $[1,N]$ can have $(1/22)N^2+O\left(N\right)$ monochromatic Schur triples, but not less.

Robertson, Aaron, and Zeilberger, Doron. "A 2-coloring of can have monochromatic Schur triples, but not less.." The Electronic Journal of Combinatorics [electronic only] 5.1 (1998): Research paper 19, 4 p.-Research paper 19, 4 p.. <http://eudml.org/doc/119532>.

@article{Robertson1998,
author = {Robertson, Aaron, Zeilberger, Doron},
journal = {The Electronic Journal of Combinatorics [electronic only]},
keywords = {colorings; Schur triple},
language = {eng},
number = {1},
pages = {Research paper 19, 4 p.-Research paper 19, 4 p.},
publisher = {Prof. André Kündgen, Deptartment of Mathematics, California State University San Marcos, San Marcos},
title = {A 2-coloring of can have monochromatic Schur triples, but not less.},
url = {http://eudml.org/doc/119532},
volume = {5},
year = {1998},
}

TY - JOUR
AU - Robertson, Aaron
AU - Zeilberger, Doron
TI - A 2-coloring of can have monochromatic Schur triples, but not less.
JO - The Electronic Journal of Combinatorics [electronic only]
PY - 1998
PB - Prof. André Kündgen, Deptartment of Mathematics, California State University San Marcos, San Marcos
VL - 5
IS - 1
SP - Research paper 19, 4 p.
EP - Research paper 19, 4 p.
LA - eng
KW - colorings; Schur triple
UR - http://eudml.org/doc/119532
ER -