"Greater": Given two vectors, x and y, we say that x>=y if xi>=yi for all i. That is, x is greater than y component-by-component.

"Increasing Difference": The function f(x,y,z) satisfies increasing differences in (x,y) if, for all x1>x2, y, and z, f(x1,y,z)-f(x2,y,z) is nondecreasing in y.

"Supermodular": A function f(x) is called supermodular in x if it satisfies increasing differences in (xi,xj) for all i<>j. In the function f(x), x is a vector.