Analytic Combinatorics: A Multidimensional Approach

Analytic Combinatorics: A Multidimensional Approach is a textbook that provides 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. It discusses objects that can be enumerated using generating functions, such as tree classes and lattice walks, and introduces multivariate generating functions. The second part explains methods of counting these objects, which involves deep mathematics from outside combinatorics, such as complex analysis and geometry.

Format: Paperback / softback
Length: 252 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Analytic Combinatorics: A Multidimensional Approach is a comprehensive textbook designed to provide a solid introduction to the field of analytic combinatorics. Written in a reader-friendly style, it aims to enhance the understanding of the concept and its applications. The book serves as a valuable tool for readers seeking to gain a deeper comprehension of the structure and large-scale behavior of discrete objects.

Primarily, the textbook serves as a gateway to the interplay between complex analysis and combinatorics. It guides readers through the connections between number theory, algebraic geometry, probability, and formal language theory.

The textbook begins by exploring objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions, including topics such as the kernel method and diagonal constructions.

The second part of the textbook delves into methods of counting these objects, which involve deep mathematics drawn from outside combinatorics, including complex analysis and geometry.

Key Features:

Combinatorics-Centric Exposition: The book employs a combinatorics-centric exposition to illustrate advanced analytic techniques. This approach makes the material more accessible and engaging for readers with a background in combinatorics.

Each chapter includes problems, exercises, and reviews of the material discussed, aiding in the consolidation of knowledge and understanding.

Comprehensive Glossary: A comprehensive glossary is provided to assist readers in navigating unfamiliar terms and concepts. Additionally, lists of figures and symbols are included to enhance visual comprehension.

About the Author:

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

Analytic Combinatorics: A Multidimensional Approach is an essential resource for students, researchers, and practitioners interested in the field of analytic combinatorics. Its comprehensive coverage, clear explanations, and engaging style make it an invaluable tool for advancing knowledge and understanding in this area.

Weight: 470g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032475134