ABSTRACT
In the last chapter, we introduced techniques for computing generating functions GS(x) =∑ z∈S x
wt(z) where S is a finite set of weighted objects. These generating functions are polynomials in the variable x. Now suppose that S is an infinite set of weighted objects. By analogy with the finite case, we would like to define a generating function GS(x) =∑
z∈S x wt(z) =
∑ n≥0 anx
n, where an is the number of objects in S of weight n. But the resulting expression GS(x) is no longer a polynomial in x, since a polynomial can have only finitely many terms.
