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Analytic combinatorics in several variables 1st Edition by Robin Pemantle, Mark C Wilson ISBN 1107031575 978-1107031579

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Analytic combinatorics in several variables Pemantle R. Digital Instant Download

Author(s): Pemantle R., Wilson M.C
ISBN(s): 9783513533548, 3513533543
Edition: draft
File Details: PDF, 2.65 MB
Year: 2012
Language: english
SKU: EB-6743204 Category: Tags: ,

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Product details:

ISBN 10: 1107031575

ISBN 13: 978-1107031579 

Author: Robin Pemantle, Mark C. Wilson 

This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. 

Table of contents:

PART I – COMBINATORIAL ENUMERATION

  • Introduction

  • Generating Functions

  • Univariate Asymptotics

PART II – MATHEMATICAL BACKGROUND

  • Fourier-Laplace Integrals in One Variable

  • Fourier-Laplace Integrals in More than One Variable

  • Techniques of Symbolic Computation via Gröbner Bases

  • Cones, Laurent Series, and Amoebas

PART III – MULTIVARIATE ENUMERATION

  • Overview of Analytic Methods for Multivariate Generating Functions

  • Smooth Point Asymptotics

  • Multiple Point Asymptotics

  • Cone Point Asymptotics

  • Worked Examples

  • Extensions

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Tags: Robin Pemantle, Mark C Wilson, Analytic Combinatorics, Several Variables