Description
Book SynopsisDiscrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such structures.
Trade Review'A definitive treatment of a challenging but very useful subject. There is a wide variety of situations calling for the estimation of the coefficients of a multivariate generating function. The authors have done a superb job of classifying and elucidating the myriad of available techniques for achieving this aim.' Richard P. Stanley, University of Miami
'This book is an invaluable resource that is certain to have dramatic impact on research and teaching in this rapidly developing area of mathematics. The first edition broke new ground; this edition prepares the field for others to harvest new knowledge with important applications in many scientific disciplines.'
Table of ContentsPart I. Combinatorial Enumeration: 1. Introduction; 2. Generating functions; 3. Univariate asymptotics; Part II. Mathematical Background: 4. Fourier–Laplace integrals in one variable; 5. Multivariate Fourier–Laplace integrals; 6. Laurent series, amoebas, and convex geometry; Part III. Multivariate Enumeration: 7. Overview of analytic methods for multivariate generating functions; 8. Effective computations and ACSV; 9. Smooth point asymptotics; 10. Multiple point asymptotics; 11. Cone point asymptotics; 12. Combinatorial applications; 13. Challenges and extensions; Appendices: A. Integration on manifolds; B. Algebraic topology; C. Residue forms and classical Morse theory; D. Stratification and stratified Morse theory; References; Author index; Subject index.
