Introductory Multidimensional Analytic Combinatorics

1st Edition

Marni Mishna

Chapman and Hall/CRC
November 5, 2019 Forthcoming
Textbook - 248 Pages - 30 B/W Illustrations
ISBN 9781138489769 - CAT# K349856
Series: Discrete Mathematics and Its Applications

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Summary

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.

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