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  3. Analytic Combinatorics in Several Variables
  • Cited by 41
Publisher:
Cambridge University Press
Online publication date:
July 2013
Print publication year:
2013
Online ISBN:
9781139381864
DOI:
https://doi.org/10.1017/CBO9781139381864
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
Series:
Cambridge Studies in Advanced Mathematics (140)
Information

Book description

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. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/ACSVbook/.

Reviews

'It deserves a place on college library shelves … it provides a nearly universal answer to the 'what can I do with this stuff?' question that students pose in so many basic courses. Recommended.'

D. V. Feldman Source: Choice

'The organization of the book is exemplary. A thorough and well-designed introduction provides full context and is worth rereading as one works through the book … The treatment of analytic methods for multivariate generating functions in this book is breathtaking. A detailed overview is followed by thorough chapters on smooth point asymptotics, multiple point asymptotics, and cone point asymptotics, then four worked examples, and extensions. The end result, a combination of analytic, Morse-theoretic, algebraic, topological, and asymptotic methods, is surprisingly effective. Indeed, it is astonishing that the authors have found relevant ways to exploit such a broad spectrum of mathematical tools to address the problem at hand.'

Robert Sedgewick Source: Bulletin of the AMS

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Contents

Contents
References
References
References
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