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Analytic Combinatorics

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

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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.

    • 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, 2019 Leroy P. Steele Prize for Mathematical Exposition, American Mathematical Society
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    Reviews & endorsements

    '… thorough and self-contained … presentation of … topics is very well organised … provides an ample amount of examples and illustrations, as well as a comprehensive bibliography. It is valuable both as a reference work for researchers working in the field and as an accessible introduction suitable for students at an advanced graduate level.' EMS Newsletter

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    Product details

    • Date Published: January 2009
    • format: Hardback
    • isbn: 9780521898065
    • length: 826 pages
    • dimensions: 254 x 178 x 45 mm
    • weight: 1.6kg
    • 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, 2019 Leroy P. Steele Prize for Mathematical Exposition, American Mathematical Society
    • Winner of the Choice Outstanding Academic Title 2009

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