[ Q(x) = \sum_i<j (x_i - x_j)^2 ]
or more combinatorially:
[ P(\mathbfx) = \sum_i=1^n \omega^x_i \quad \text(where $\omega$ is a primitive 3rd root of unity) ] polymath 6.1 key
[ \textKey function: f(x) = \text(# of 0's) - \text(# of 1's) \quad \textmod something? ] [ Q(x) = \sum_i<j (x_i - x_j)^2 ]
For precise algebraic form, consult the (section “Key lemma” or “Key polynomial”) or the final paper: “Density Hales-Jewett and Moser numbers” (2012). [ Q(x) = \sum_i<