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.

part I|1 pages

Enumerative Combinatorics

chapter 1|32 pages

A Primer on Combinatorial Calculus

chapter 2|19 pages

Combinatorial Parameters

chapter 3|23 pages

Derived and Transcendental Classes

part II|1 pages

Methods for Asymptotic Analysis

chapter 4|30 pages

Generating Functions as Analytic Objects

chapter 5|28 pages

Parallel Taxonomies

chapter 8|14 pages

Multiple Points

chapter 9|22 pages