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Analytic Combinatorics in Several Variables
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Artikel-Nr:
9781108836623
Veröffentl:
2024
Einband:
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Erscheinungsdatum:
30.01.2024
Seiten:
592
Autor:
Robin Pemantle
Gewicht:
1102 g
Format:
235x157x39 mm
Sprache:
Englisch
Beschreibung:
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.
"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"--
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.