Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick

Analytic Combinatorics

Buch | Hardcover
826 Seiten
2009
Cambridge University Press (Verlag)
978-0-521-89806-5 (ISBN)
99,95 inkl. MwSt
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.
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.

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.

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.

Erscheint lt. Verlag 15.1.2009
Zusatzinfo Worked examples or Exercises; 50 Tables, unspecified; 74 Halftones, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 178 x 254 mm
Gewicht 1600 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-521-89806-4 / 0521898064
ISBN-13 978-0-521-89806-5 / 9780521898065
Zustand Neuware
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