Analytic Combinatorics

by Philippe Flajolet, Robert Sedgewick

Overview

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Product Details

ISBN-13:	9780521898065
Publisher:	Cambridge University Press
Publication date:	01/15/2009
Edition description:	New Edition
Pages:	826
Product dimensions:	6.70(w) x 9.80(h) x 1.80(d)

About the Author

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.

Table of Contents

Preface; An invitation to analytic combinatorics; Part A. Symbolic Methods: 1. Combinatorial structures and ordinary generating functions; 2. Labelled structures and exponential generating functions; 3. Combinatorial parameters and multivariate generating functions; Part B. Complex Asymptotics: 4. Complex analysis, rational and meromorphic asymptotics; 5. Applications of rational and meromorphic asymptotics; 6. Singularity analysis of generating functions; 7. Applications of singularity analysis; 8. Saddle-Point asymptotics; Part C. Random Structures: 9. Multivariate asymptotics and limit laws; Part D. Appendices: Appendix A. Auxiliary elementary notions; Appendix B. Basic complex analysis; Appendix C. Concepts of probability theory; Bibliography; Index.

What People are Saying About This

From the Publisher

"... this is a valuable, comprehensive treatment."
Angele M. Hamel, reviews.com

"... certain to become the standard reference book of the field. While Analytical Combinatorics has more than enough information to become a reference book, it is also written in a reader-friendly style that makes it appropriate as a course resource. In the past, it was not always clear what "analytic combinatorics" meant; this book will bring about a consensus on that question."
M. Bona, Choice Magazine

"Because of the breadth, and depth of topical coverage, the highly applicable results and the enjoyable writing that characterize this book, Analytic Combinatorics is now defined. The authors wrote the book on it."
Miklos Bona, SIGNACT News

Editorial Reviews

"... this is a valuable, comprehensive treatment."
Angele M. Hamel, reviews.com

"... certain to become the standard reference book of the field. While Analytical Combinatorics has more than enough information to become a reference book, it is also written in a reader-friendly style that makes it appropriate as a course resource. In the past, it was not always clear what "analytic combinatorics" meant; this book will bring about a consensus on that question."
M. Bona, Choice Magazine

"Because of the breadth, and depth of topical coverage, the highly applicable results and the enjoyable writing that characterize this book, Analytic Combinatorics is now defined. The authors wrote the book on it."
Miklos Bona, SIGNACT News

From the Publisher