Analytic combinatorics

Summary

Analytic combinatorics finds the asymptotic size of combinatorial counts from their generating functions, see the definition. It views a generating function as a function of a complex variable. The singularities closest to the origin decide the exponential growth of the coefficients, and the type of these singularities decides the correction factor. Together with the symbolic method, it is the subject of the book "Analytic Combinatorics" by Philippe Flajolet and Robert Sedgewick.