Analytic Combinatorics in Several Variables

Robin Pemantle, Mark C. Wilson (Autoren)

Buch | Hardcover

392 Seiten

2013
Cambridge University Press (Verlag)
978-1-107-03157-9 (ISBN)

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This book is the result of nearly fifteen years work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.

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/.

Robin Pemantle is a Professor in the Department of Mathematics at the University of Pennsylvania. Mark C. Wilson is a Senior Lecturer in the Department of Computer Science at the University of Auckland.

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.

Reihe/Serie	Cambridge Studies in Advanced Mathematics
Zusatzinfo	Worked examples or Exercises; 2 Tables, unspecified; 4 Halftones, unspecified; 49 Line drawings, unspecified
Verlagsort	Cambridge
Sprache	englisch
Maße	156 x 235 mm
Gewicht	660 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-107-03157-5 / 1107031575
ISBN-13	978-1-107-03157-9 / 9781107031579
Zustand	Neuware