Philippe Flajolet: Analytic Combinatorics

Cover: 9780521898065 | Analytic Combinatorics | Philippe Flajolet (u. a.) | Buch | Englisch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2015
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521898065
ISBN-10:	0521898064
Sprache:	Englisch
Einband:	Gebunden
Autor:	Flajolet, Philippe Sedgewick, Robert
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	250 x 175 x 48 mm
Von/Mit:	Philippe Flajolet (u. a.)
Erscheinungsdatum:	02.03.2015
Gewicht:	1,577 kg