Lesson 4

Despite the simplicity of this example, it demonstrates two important ideas of generating functions:

• We are only interested in the coefficients of this polynomial, and we are not going to substitute anything for the variable \(x\) (hence it is called formal).


• The multiplication of polynomials naturally corresponds to selecting one element from each of the sets. (These two polynomials, in fact, are generating functions of the respective sets. If we wanted to select no more than one element from each of them, we could add a constant term to the corresponding polynomials.)