Analytic Combinatorics

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Cambridge University Press, Jan 15, 2009 - Mathematics
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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. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
 

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quite a good book specially the part on words and generating functions..........

Contents

An Invitation to Analytic Combinatorics
3
Combinatorial Structures and Ordinary Generating Functions
15
Labelled Structures and Exponential Generating Functions
95
Combinatorial Parameters and Multivariate Generating Functions
151
Complex Analysis Rational and Meromorphic Asymptotics
223
Applications of Rational and Meromorphic Asymptotics
289
Singularity Analysis of Generating Functions
375
Applications of Singularity Analysis
439
Auxiliary Elementary Notions
721
Basic Complex Analysis
739
Holonomic functions
748
Laplaces method
755
Mellin transforms
762
Concepts of Probability Theory
769
Bibliography
779
endix
795

Saddlepoint Asymptotics
541
EX Multivariate Asymptotics and Limit Laws
611

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About the author (2009)

Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt.

Robert Sedgewick is William O. Baker Professor of Computer Science at Princeton University, New Jersey.

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