Analytic Combinatorics in Several Variables
1st Edition
Published on 31. May 2013
978-1-107-24051-3 (ISBN)
Description
This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/ACSVbook/.
Reviews / Votes
'It deserves a place on college library shelves ... it provides a nearly universal answer to the 'what can I do with this stuff?' question that students pose in so many basic courses. Recommended.' D. V. Feldman, Choice 'The organization of the book is exemplary. A thorough and well-designed introduction provides full context and is worth rereading as one works through the book ... The treatment of analytic methods for multivariate generating functions in this book is breathtaking. A detailed overview is followed by thorough chapters on smooth point asymptotics, multiple point asymptotics, and cone point asymptotics, then four worked examples, and extensions. The end result, a combination of analytic, Morse-theoretic, algebraic, topological, and asymptotic methods, is surprisingly effective. Indeed, it is astonishing that the authors have found relevant ways to exploit such a broad spectrum of mathematical tools to address the problem at hand.' Robert Sedgewick, Bulletin of the AMSMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 2 Tables, unspecified; 4 Halftones, unspecified; 49 Line drawings, unspecified
File size
5,62 MB
ISBN-13
978-1-107-24051-3 (9781107240513)
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Schweitzer Classification
Other editions
Additional editions
Robin Pemantle | Mark C. Wilson
Analytic Combinatorics in Several Variables
Book
05/2013
Cambridge University Press
€68.08
Article exhausted; check for reprint
Persons
Robin Pemantle is a Professor in the Department of Mathematics at the University of Pennsylvania. Mark C. Wilson is a Senior Lecturer in the Department of Computer Science at the University of Auckland.
Content
Part I. Combinatorial Enumeration: 1. Introduction; 2. Generating functions; 3. Univariate asymptotics; Part II. Mathematical Background: 4. Saddle integrals in one variable; 5. Saddle integrals in more than one variable; 6. Techniques of symbolic computation via Grobner bases; 7. Cones, Laurent series and amoebas; Part III. Multivariate Enumeration: 8. Overview of analytic methods for multivariate generating functions; 9. Smooth point asymptotics; 10. Multiple point asymptotics; 11. Cone point asymptotics; 12. Worked examples; 13. Extensions; Part IV. Appendices: Appendix A. Manifolds; Appendix B. Morse theory; Appendix C. Stratification and stratified Morse theory.
