Analytic Combinatorics

The definitive treatment of analytic combinatorics, from leaders in the field. Exercises, examples, appendices and notes aid understanding.

Informationen zum Autor Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt. Robert Sedgewick is William O. Baker Professor of Computer Science at Princeton University. Klappentext The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures! with thorough treatment of a large number of applications. Exercises! examples! appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses. Zusammenfassung The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures! with thorough treatment of a large number of applications. Exercises! examples! appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses.

Autorentext
Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt.Robert Sedgewick is William O. Baker Professor of Computer Science at Princeton University, New Jersey.

Zusammenfassung
The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large number of applications. Exercises, examples, appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses.

Inhalt
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.

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