Analytic combinatorics in several variables

"Discrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such...

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Bibliographische Detailangaben
1. Verfasser:	Pemantle, Robin (VerfasserIn)
Weitere Verfasser:	Wilson, Mark C. (VerfasserIn), Melczer, Stephen (VerfasserIn)
Format:	UnknownFormat
Sprache:	eng
Veröffentlicht:	Cambridge, United Kingdom, New York, NY , USA Cambridge University Press 2024
Ausgabe:	Second edition
Schriftenreihe:	Cambridge studies in advanced mathematics 212
Schlagworte:	Combinatorial enumeration problems > Functions of several complex variables > MATHEMATICS / Discrete Mathematics > Abzählende Kombinatorik > Mehrere komplexe Variable > Erzeugende Funktion > Laurent-Entwicklung > Asymptotische Entwicklung > Kritischer Punkt > Morse-Theorie
Online Zugang:	Inhaltsverzeichnis zbMATH
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Beschreibung
Zusammenfassung:	"Discrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such structures"-- Publisher’s description: Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.
Beschreibung:	Literaturverzeichnis: Seite 533-551
Beschreibung:	xix, 571 Seiten Illustrationen, Diagramme
ISBN:	9781108836623 978-1-108-83662-3