Robin Pemantle, Mark C. Wilson, Stephen Melczer

Analytic Combinatorics in Several Variables

• Gebundenes Buch

Produktbeschreibung

"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"--

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 592
• Erscheinungstermin: 30. Januar 2024
• Englisch
• Abmessung: 235mm x 157mm x 39mm
• Gewicht: 1100g
• ISBN-13: 9781108836623
• ISBN-10: 1108836623
• Artikelnr.: 69521786

Autorenporträt

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.