Analytic Combinatorics
Analytic Combinatorics
Robert Sedgewick, Princeton University, New Jersey
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USDAnalytic 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
Awards
Winner, 2019 Leroy P. Steele Prize for Mathematical Exposition, American Mathematical Society
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
Product details
January 2009Hardback
9780521898065
826 pages
254 × 178 × 45 mm
1.6kg
74 b/w illus. 50 tables
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.
