Analytic Combinatorics

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. Symbolic Methods -- Combinatorial Structures And Ordinary Generating Functions -- Labelled Structures And Exponential Generating Functions -- Combinatorial Parameters And Multivariate Generating Functions -- Complex Asymptotics -- Complex Analysis, Rational And Meromorphic Asymptotics -- Applications Of Rational And Meromorphic Asymptotics -- Singularity Analysis Of Generating Functions -- Applications Of Singularity Analysis -- Saddle-point Asymptotics -- Random Structures -- Multivariate Asymptotics And Limit Laws -- Appendix A : Auxiliary Elementary Notions -- Appendix B : Basic Complex Analysis -- Appendix C : Concepts Of Probability Theory. Philippe Flajolet & Robert Sedgewick. Includes Bibliographical References (p. 779-800) And Index. "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. In order to make it self-contained, the authors provide full coverage of the underlying mathematics and give a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes throughout the book to aid understanding. The book can be used as a reference for researchers, as a textbook for an advanced undergraduate or a graduate course on the subject, or for self-study."--Page 4 of cover "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. In order to make it self-contained, the authors provide full coverage of the underlying mathematics and give a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes throughout the book to aid understanding. The book can be used as a reference for researchers, as a textbook for an advanced undergraduate or a graduate course on the subject, or for self-study."--Jacket 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.