Analytic combinatorics in several variables
 Responsibility
 Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.
 Language
 English.
 Publication
 Cambridge : Cambridge University Press, 2013.
 Physical description
 xiii, 380 pages : illustrations ; 24 cm.
 Series
 Cambridge studies in advanced mathematics ; 140.
Access
Creators/Contributors
 Author/Creator
 Pemantle, Robin.
 Contributor
 Wilson, Mark C. (Mark Curtis), 1967
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 363371) and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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/ACSVb ook/.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2013
 Series
 Cambridge studies in advanced mathematics ; 140
 ISBN
 9781107031579 (hardback)
 1107031575 (hardback)