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Analytic Combinatorics

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  • Date Published: January 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521898065

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About the Authors
  • 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.

    • Comprehensive: generous notes, appendices, examples and exercises, as well as the inclusion of proofs of fundamental results
    • Unified: ties together classical mathematics and modern applications
    • Cutting edge: first book with extensive coverage of analytic methods needed to analyse large combinatorial configurations
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    Awards

    • Winner of the Choice Outstanding Academic Title 2009

    Reviews & endorsements

    "... 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

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    Product details

    • Date Published: January 2009
    • format: Hardback
    • isbn: 9780521898065
    • length: 826 pages
    • dimensions: 249 x 178 x 43 mm
    • weight: 1.56kg
    • contains: 74 b/w illus. 50 tables
    • availability: Available
  • 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.

  • Resources for

    Analytic Combinatorics

    Philippe Flajolet, Robert Sedgewick

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  • Authors

    Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt
    Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt.

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

    Awards

    • Winner of the Choice Outstanding Academic Title 2009

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