Analytic combinatorics

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Analytic combinatorics is a sub-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.