The grid of dimension d and side n, denoted G(d, n), is the set of all d-tuples ...

The grid of dimension d and side n, denoted G(d, n), is the set of all d-tuples (x1, ... , Xa) such that the x;'s are integers between 0 and n 1. A monotone function f is a function from G(d, n) to itself such that if x