Symbolic Enumeration

Generating functions provide a standard tool for enumeration. In this chapter we combine the use of generating functions with the so-called symbolic method which provides a simple systematic way of obtaining the generating function of a class of combinatorial objects by a symbolic description of the class. Generating functions can be thought of as analytic complex functions or can be viewed simply as formal power series, by disregarding convergence issues. Although we will not completely ignore the analytic perspective, we will mostly adopt this latter point of view. Basic definitions and results on formal power series are included, which includes the useful Lagrange inversion formula.