Analytic combinatorics in several variables
著者
書誌事項
Analytic combinatorics in several variables
（Cambridge studies in advanced mathematics, 140）
Cambridge University Press, 2013
- : hardback
大学図書館所蔵 全36件
注記
Includes bibliographical references (p. 363-371) and indexes
内容説明・目次
内容説明
This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/ACSVbook/.
目次
- 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.
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