Analytic Combinatorics

Analytic Combinatorics

Analytic Combinatorics covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large number of applications.


Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic.

Table of Contents

  • Combinatorial Structures and Ordinary Generating Functions
  • Labelled Structures and Exponential Generating Functions
  • Combinatorial Parameters and Multivariate Generating Functions
  • Complex Analysis, Rational and Meromorphic Asymptotics
  • Applications of Rational and Meromorphic Asymptotics
  • Singularity Analysis of Generating Functions
  • Applications of Singularity Analysis
  • Saddle-Point Asymptotics
  • Multivariate Asymptotics and Limit Laws

Book Details

Author(s): Philippe Flajolet and Robert Sedgewick
Publisher: Cambridge University Press
Format(s): PDF
File size: 11.58 MB
Number of pages: 826
Link: Analytic Combinatorics [PDF].

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