Analytic combinatorics in several variables Robin Pemantle, Mark C. Wilson
Material type: TextSeries: Cambridge studies in advanced mathematics ; 140Publication details: Cambrdige Cambrdige University Press 2013Description: xiii, 380 pages ; 24 cmISBN:- 9781107031579 (hardback)
- 511.6 PEM 23rd
- MAT008000
Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
Books | North Eastern Hill University General Stacks | MATHEMATICS | 511.6 PEM (Browse shelf(Opens below)) | Available | 420209 |
Browsing North Eastern Hill University shelves, Shelving location: General Stacks, Collection: MATHEMATICS Close shelf browser (Hides shelf browser)
511.6 HAR Combinatorics and graph theory | 511.6 LAN Ramsey theory on the integers | Course in topological combinatorics | 511.6 PEM Analytic combinatorics in several variables | 511.6 PER Combinatorial methods | 511.6 PER Combinatorial methods | 511.6 PRO Ramsey theory for discrete structures |
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"--
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