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
2 - Generating functions
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 chapter covers standard material on generating functions in one and several variables. We describe how many common combinatorial constructions yield generating function specifications, often leading to rational or algebraic equations for generating functions. We also cover D-finite generating functions, which satisfy linear differential equations and arise both from linearly recurrent sequences and as diagonals of rational generating functions. Finally, we discuss labeled combinatorial constructions and exponential generating functions.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 17 - 59Publisher: Cambridge University PressPrint publication year: 2024