Analytic combinatorics : a multidimensional approach - Mishna, Marni (Boca Raton : Chapman & Hall/CRC, 2019)
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 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
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Keywords: Combinatorial analysis; MATHEMATICS / General; MATHEMATICS / Combinatorics