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Analytic Combinatorics

Details

  • 74 b/w illus. 50 tables
  • Page extent: 826 pages
  • Size: 247 x 174 mm
  • Weight: 1.56 kg

Library of Congress

  • Dewey number: 511.6
  • Dewey version: 22
  • LC Classification: n/a
  • LC Subject headings:
    • Combinatorial analysis
    • Combinatieleer.--gtt

Library of Congress Record

Hardback

 (ISBN-13: 9780521898065)

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

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.

Prize Winner

Choice Outstanding Academic Title 2009 - Winner

Review

'… 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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