Mishna M. Analytic Combinatorics: A Multidimensional Approach

Chapman and Hall/CRC, CRC Press; Taylor & Francis Group, 2020. — 252 p. — (Discrete Mathematics and Its Applications). — ISBN13: 978-1-138-48976-9.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.
Features
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
Contents
Enumerative Combinatorics
A Primer on Combinatorial Calculus
Combinatorial Parameters
Derived and Transcendental Classes
Methods for Asymptotic Analysis
Generating Functions as Analytic Objects
Parallel Taxonomies
Singularities of Multivariable Rational Functions
Integration and Multivariable Coefficient Asymptotics
Multiple Points
Partitions