"Discrete 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"--
"Discrete 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"--
Robin Pemantle is Merriam Term Professor of Mathematics at the University of Pennsylvania, working in the fields of probability theory and combinatorics. He received his bachelor's degree from Berkeley and his Ph.D. from MIT. He is a Fellow of the AMS and IMS and a winner of the Rollo Davidson Prize.
Inhaltsangabe
Part 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.
Part 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.
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