Analytic combinatorics: a multidimensional approach

by Mishna, Marni

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Title Statements

Full title :Analytic combinatorics : a multidimensional approach / Marni Mishna.

Summary

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.

Edition Statements

Publication Date:2020.

Publication Statements

Publisher(s):CRC Press
Place of Publication:Boca Raton, FL
Language:eng
Publication Date:2020.

Notes

"A Chapman & Hall book."

The Physical Object

Description:1 online resource (xxi, 229 pages) : : illustrations (black and white)

Edition Identifiers

ISBN:9781351036801, 1351036807, 9781351036818, 1351036815, 9781351036825, 1351036823, 9781351036795, 1351036793
DOI:10.1201/9781351036825
oclc:on1129672805
LC Classification:QA164
Dewey Decimal:511/.6

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.

I. Enumerative combinatorics. 1. A primer on combinatorial calculus ; 2. Combinatorial parameters ; 3. Derived and transcendental classes -- II. Methods for asymptotic analysis. 4. Generating functions as analytic objects ; 5. Parallel taxonomies ; 6. Singularities of multivariable rational functions ; 7. Integration and multivariable coefficient asymptotics ; 8. Multiple points ; 9. Partitions.