California State University, Northridge WordmarkOviatt Library WordmarkOviatt Library Catalog Wordmark
Author Pemantle, Robin.
Title Analytic combinatorics in several variables / Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.
Published Cambridge : Cambridge University Press, 2013.
Book Cover

 Floor4  QA164.8 .P46 2013    IN LIBRARY
Description xiii, 380 pages ; 24 cm.
Content Type text
Format volume
Series Cambridge studies in advanced mathematics ; 140
Cambridge studies in advanced mathematics ; 140.
Bibliography Includes bibliographical references (pages 363-371) and indexes.
Contents 1. Introduction -- 2. Generating functions -- 3. Univariate asymptotics -- 4. Fourier-Laplace integrals in one variable -- 5. Fourier-Laplace integrals in more than one variable -- 6. Techniques of symbolic computation via Gröbner bases -- 7. Cones, Laurent series and amoebas -- 8. Overview of analytic methods for multivariate generating functions -- 9. Smooth point asymptotics --10. Multiple point asymptotics --11. Cone point asymptotics --12. Worked examples -- 13. Extensions -- Appendices.
Summary "Mathematicians have found it useful to enumerate all sorts of things arising in discrete mathematics: elements of finite groups, configurations of ones and zeros, graphs of various sorts; the list is endless. Analytic combinatorics uses analytic techniques to do the counting: generating functions are defined and their coefficients are then estimated via complex contour integrals. This book is the result of nearly fifteen years work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable"-- Provided by publisher.
Subject Combinatorial enumeration problems.
Functions of several complex variables.
Related Names Wilson, Mark C. (Mark Curtis), 1967-
ISBN 1107031575 (hardback)
9781107031579 (hardback)
OCLC number 830030004