Analytic Combinatorics

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Philippe Flajolet, Robert SedgewickCambridge University Press, 1/15/2009EAN 9780521898065, ISBN10: 0521898064Hardcover, 826 pages, 24.7 x 17.4 x 4.3 cmLanguage: EnglishAnalytic com binatorics 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.PrefaceAn invitation to analytic combinatoricsPart A. Symbolic Methods1. Combinatorial structures and ordinary generating functions2. Labelled structures and exponential generating functions3. Combinatorial parameters and multivariate generating functionsPart B. Complex Asymptotics4. Complex analysis, rational and meromorphic asymptotics5. Applications of rational and meromorphic asymptotics6. Singularity analysis of generating functions7. Applications of singularity analysis8. Saddle-Point asymptoticsPart C. Random Structures9. Multivariate asymptotics and limit lawsPart D. AppendicesAppendix A. Auxiliary elementary notionsAppendix B. Basic complex analysisAppendix C. Concepts of probability theoryBibliographyIndex.'… 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 Show more