Analytic combinatorics

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.

[edit] References

• Herbert Wilf, Generatingfunctionology, Academic Press, 1990, ISBN 0127519556.
• Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge University Press, 2008, ISBN 0521898064 (Not published yet).

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