# Analytic combinatorics in several variables / Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.

##### By: Pemantle, Robin.

##### Contributor(s): Wilson, Mark C. (Mark Curtis).

Material type: TextSeries: Cambridge studies in advanced mathematics ; 140.Description: xiii, 380 pages, UKP 45.00 24 cm.ISBN: 9781107031579 (hardback).Subject(s): Combinatorial enumeration problems | Functions of several complex variables | MATHEMATICS / Discrete MathematicsDDC classification: 511/.6 Other classification: MAT008000 Online resources: Cover imageItem type | Current location | Call number | Status | Date due | Barcode | Item holds |
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Book | Chennai Mathematical Institute General Stacks | 511.6 PEM (Browse shelf) | Available | 8853 |

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Includes bibliographical references (pages 363-371) and indexes.

Machine generated contents note: 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.

"Mathematicians have found it useful to enumerate all sorts of things arising in discrete mathematics: elements of finite groups, configurations of ones and zeros, graphs of various sorts; the list is endless. Analytic combinatorics uses analytic techniques to do the counting: generating functions are defined and their coefficients are then estimated via complex contour integrals. This book is the result of nearly fifteen years work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable"--