Introductory Multidimensional Analytic Combinatorics: 1st Edition (Hardback) book cover

Introductory Multidimensional Analytic Combinatorics

1st Edition

By Marni Mishna

Chapman and Hall/CRC

248 pages | 30 B/W Illus.

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Hardback: 9781138489769
pub: 2019-11-05
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Description

The text starts by discussing the objects that can be enumerated using multivariate generating functions, such as permutations, maps, and lattice walks. The author is an expert on the last example. She will also introduce multivariate generating functions, and have a section about the Kernel method (a topic so vaste that Thomas Prellberg is considering a book forus on it). She will also discuss diagonals. The second part explains the methods of counting these objects. This will involve deep mathematics coming from outside combinatorics, such as complex analysis and topology. It is the need for these tools that makes the topic so difficult, so here the presentation will be reader-friendly.

Table of Contents

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

Case Study: Partitions

About the Author

Marni Mishna is a professor of mathematics at Simon Fraser University, BC, Canada

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT036000
MATHEMATICS / Combinatorics