Analytic Combinatorics

ISBN-13: 9780521898065 / Angielski / Twarda / 2009 / 826 str.

Philippe Flajolet; Robert Sedgewick

Opis

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Recenzje

'... 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

Spis treści

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.

O autorze

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