Description
Analytic Combinatorics
A Multidimensional Approach
Discrete Mathematics and Its Applications Series
Author: Mishna Marni
Language: English
Subject for Analytic Combinatorics:
Keywords
Standard Young Tableaux; Dyck Paths; Subexponential Growth; Coefficient Asymptotics; Laurent Series Expansion; Admissible Operators; Algebraic Independence; Motzkin Paths; Finite Root System; Ordinary Generating Function; Singular Variety; Cauchy Integral; Context Free Language; Series Expansion; Transversal Intersection; Formal Power Series; Combinatorial Classes; Lattice Walks; Cumulative Generating Function; Cayley Graph; Puiseux Expansion; Finite Reflection Groups; Vector Partitions; Hyperplane Arrangement; Dominant Singularity
Publication date: 01-2023
· 15.6x23.4 cm · Paperback
Publication date: 11-2019
· 15.6x23.4 cm · Hardback
Description
/li>Contents
/li>Biography
/li>
Analytic Combinatorics: A Multidimensional Approachis 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
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
Partitions
Bibliography
Glossary
Index
