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.
Famous quotes containing the word analytic:
““You, that have not lived in thought but deed,
Can have the purity of a natural force,
But I, whose virtues are the definitions
Of the analytic mind, can neither close
The eye of the mind nor keep my tongue from speech.””
—William Butler Yeats (1865–1939)