Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, with formal power series that often correspond to analytic functions.
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 singularities of the associated analytic function.
Two types of generating functions are commonly used — ordinary and exponential generating functions.
An important technique for deriving generating functions is symbolic combinatorics.
Analytic combinatorics is a calculus for the quantitative study of large combinatorial structures.
References
- Herbert Wilf, Generatingfunctionology, Academic Press, 1990, ISBN 0-12-751955-6.
- Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge University Press, 2008, ISBN 0-521-89806-4, Free online version of the book.
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