Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, which are often analytic functions, but sometimes formal power series. Two types of generating functions are commonly used — ordinary and exponential generating functions. An important technique for deriving generating functions is symbolic combinatorics. Given a generating function, analytic combinatorics attempts to describe the asymptotic behavior of a counting sequence using algebraic techniques. This often involves analysis of the function's singularities.
