Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- 1 Introduction
- 2 Generating functions
- 3 Univariate asymptotics
- Part II Mathematical Background
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
1 - Introduction
from Part I - Combinatorial Enumeration
Published online by Cambridge University Press: 08 February 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- 1 Introduction
- 2 Generating functions
- 3 Univariate asymptotics
- Part II Mathematical Background
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
Summary
This first chapter motivates our detailed study of the behavior of multivariate sequences, and overviews the techniques we derive using the Cauchy Integral Formula, residues, topological arguments, and asymptotic approximations. Basic asymptotic notation and concepts are introduced, including the background necessary to discuss multivariate expansions.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 3 - 16Publisher: Cambridge University PressPrint publication year: 2024