Analytic Combinatorics: A Multidimensional Approach, 1st Edition (Hardback) book cover

Analytic Combinatorics

A Multidimensional Approach, 1st Edition

By Marni Mishna

Chapman and Hall/CRC

232 pages | 30 B/W Illus.

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Hardback: 9781138489769
pub: 2019-11-25
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Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand discrete objects. Primarily, the textbook is a gateway to more detailed and involved study and the topics covered such as the interactions between complex analysis and combinatorics will lead readers through number theory, algebraic geometry, probability, and formal language theory.

The textbook starts by discussing objects that can be enumerated using multivariate generating functions, such as permutations, maps, and lattice walks. It also introduces multivariate generating functions and includes a section about the vast topic of the Kernel method, and it discusses diagonals in depth. The second part explains the methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and topology.


  • Written with combinatorics-centric exposition to illustrate advanced analytic techniques.
  • Each chapter includes problems, exercises, and reviews of the material discussed in them
  • Includes a comprehensive glossary, as well as lists of figures and symbols

Table of Contents

A Primer on Combinatorical Calculus

Combinatorical Parameters

Derived and Transcendental Classes

Generating Functions as Analytic Objects

Parallel Taxonomies

Singularities of Multvariable Rational Functions

Integration and Multivariable Coefficient Asymptotics

Multiple Points





About the Author

Marni Mishna is a professor of mathematics at Simon Fraser University, BC, Canada

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Combinatorics