Analytic Combinatorics
Cambridge University Press, 1/15/2009
EAN 9780521898065, ISBN10: 0521898064
Hardcover, 826 pages, 24.7 x 17.4 x 4.3 cm
Language: English
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.
'… 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