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

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"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 a...

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Bibliographic Details
Main Author: Pemantle, Robin
Other Authors: Wilson, Mark C. (Mark Curtis), 1967-
Language:English
Published: Cambridge : Cambridge University Press, 2013.
Series:Cambridge studies in advanced mathematics ; 140.
Subjects:
Combinatorial enumeration problems.
Functions of several complex variables.
MATHEMATICS / Discrete Mathematics.
Physical Description:xiii, 380 pages ; 24 cm.
Format: Book
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.