Analytic Combinatorics in Several Variables

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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• Ciência da Computação
• Teoria combinatória e dos grafos