Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- Part III Multivariate Enumeration
- 7 Overview of analytic methods for multivariate GFs
- 8 Effective computations and ACSV
- 9 Smooth point asymptotics
- 10 Multiple point asymptotics
- 11 Cone point asymptotics
- 12 Combinatorial applications
- 13 Challenges and extensions
- 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
10 - Multiple point asymptotics
from Part III - Multivariate 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
- Part II Mathematical Background
- Part III Multivariate Enumeration
- 7 Overview of analytic methods for multivariate GFs
- 8 Effective computations and ACSV
- 9 Smooth point asymptotics
- 10 Multiple point asymptotics
- 11 Cone point asymptotics
- 12 Combinatorial applications
- 13 Challenges and extensions
- 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 derives asymptotics determined by a critical point near which the singular variety is locally a union of smooth complex manifolds. Several explicit formulae for asymptotics are given, depending on the dimension and number of sheets meeting at the critical point.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 291 - 338Publisher: Cambridge University PressPrint publication year: 2024