Analytic combinatorics in several variables
 Author/Creator
 Pemantle, Robin.
 Language
 English.
 Publication
 Cambridge : Cambridge University Press, 2013.
 Physical description
 xiii, 380 pages : illustrations ; 24 cm.
 Series
 Cambridge studies in advanced mathematics ; 140.
Access
Available online

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QA164.8 .P46 2013

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QA164.8 .P46 2013
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Contributors
 Contributor
 Wilson, Mark C. (Mark Curtis), 1967
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 363371) and index.
 Contents

 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.
 Summary
 "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" Provided by publisher.
Bibliographic information
 Publication date
 2013
 Responsibility
 Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.
 Series
 Cambridge studies in advanced mathematics ; 140
 ISBN
 9781107031579
 1107031575