1st Edition

Analytic Combinatorics A Multidimensional Approach

By Marni Mishna Copyright 2020
    252 Pages 30 B/W Illustrations
    by CRC Press

    252 Pages 30 B/W Illustrations
    by Chapman & Hall

    252 Pages 30 B/W Illustrations
    by Chapman & Hall

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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 the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory.

    The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry.


    • 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

    About the author

    Marni Mishna is a professor of mathematics at Simon Fraser University in British Columbia. Her research investigates interactions between discrete structures and many diverse areas such as representation theory, functional equation theory, and algebraic geometry. Her specialty is the development of analytic tools to study the large-scale behavior of discrete objects.

    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






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