Analytic Combinatorics The definitive treatment of analytic combinatorics, from leaders in the field. Exercises, examples, appendices and notes aid understanding. Philippe Flajolet (Author), Robert Sedgewick (Author) 9780521898065, Cambridge University Press Hardback, published 15 January 2009 826 pages, 74 b/w illus. 50 tables25.4 x 17.8 x 4.5 cm, 1.6 kg '… 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 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. 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. Subject Areas: Mathematical theory of computation [UYA], Combinatorics & graph theory [PBV]
