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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Analytic Combinatorics in Several Variables, Hardcover by Pemantle, Robin; Wilson, Mark C.; Melczer, Stephen, ISBN 1108836623, ISBN-13 9781108836623, Brand New, Free shipping in the US 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.
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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
Publication NameAnalytic Combinatorics in Several Variables
LanguageEnglish
Publication Year2024
SubjectGeneral, Discrete Mathematics
FeaturesRevised
TypeTextbook
Subject AreaMathematics
AuthorMark C. Wilson, Stephen Melczer, Robin Pemantle
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
Dewey Edition23/eng/20231117
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
Series Volume NumberSeries Number 212
IllustratedYes
Dewey Decimal511/.6
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.
Edition DescriptionRevised edition
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
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