Symbolic method

Summary

The symbolic method translates a description of a combinatorial class into an equation for its generating function, see the definition. Each construction, such as disjoint union, pair or sequence, has a fixed rule that acts on generating functions. Unlabelled classes lead to ordinary generating functions, and labelled classes lead to exponential generating functions. It is the first part of analytic combinatorics, whose second part extracts asymptotics from the equations.