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Cambridge Studies in Advanced Mathematics Ser.: Analytic Combinatorics in Several Variables by Mark C. Wilson, Stephen Melczer and Robin Pemantle (2024, Hardcover)

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About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101108836623

ISBN-139781108836623

eBay Product ID (ePID)6064429799

Product Key Features

Number of Pages592 Pages

LanguageEnglish

Publication NameAnalytic Combinatorics in Several Variables

SubjectGeneral, Discrete Mathematics

Publication Year2024

FeaturesRevised

TypeTextbook

AuthorMark C. Wilson, Stephen Melczer, Robin Pemantle

Subject AreaMathematics

SeriesCambridge Studies in Advanced Mathematics Ser.

FormatHardcover

Dimensions

Item Height1.5 in

Item Length9.3 in

Item Width6.2 in

Additional Product Features

Edition Number2

LCCN2023-051039

Reviews'A definitive treatment of a challenging but very useful subject. There is a wide variety of situations calling for the estimation of the coefficients of a multivariate generating function. The authors have done a superb job of classifying and elucidating the myriad of available techniques for achieving this aim.' Richard P. Stanley, University of Miami, 'This book is an invaluable resource that is certain to have dramatic impact on research and teaching in this rapidly developing area of mathematics. The first edition broke new ground; this edition prepares the field for others to harvest new knowledge with important applications in many scientific disciplines.' Robert Sedgewick, Princeton University

Dewey Edition23/eng/20231117

Series Volume NumberSeries Number 212

IllustratedYes

Dewey Decimal511/.6

Edition DescriptionRevised edition

Table Of ContentPart I. Combinatorial Enumeration: 1. Introduction; 2. Generating functions; 3. Univariate asymptotics; Part II. Mathematical Background: 4. Fourier-Laplace integrals in one variable; 5. Multivariate Fourier-Laplace integrals; 6. Laurent series, amoebas, and convex geometry; Part III. Multivariate Enumeration: 7. Overview of analytic methods for multivariate generating functions; 8. Effective computations and ACSV; 9. Smooth point asymptotics; 10. Multiple point asymptotics; 11. Cone point asymptotics; 12. Combinatorial applications; 13. Challenges and extensions; Appendices: A. Integration on manifolds; B. Algebraic topology; C. Residue forms and classical Morse theory; D. Stratification and stratified Morse theory; References; Author index; Subject index.

SynopsisDiscrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview., Discrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such structures.

LC Classification NumberQA164.8.P46 2024