An Invitation to Analytic Combinatorics
From One to Several Variables
Authors: Melczer, Stephen
Free Preview- Interactive computer algebra worksheets allow deeper understanding of the material
- Many fully worked detailed examples help to illustrate advanced theoretical methods
- Unique blend of theory, computation, and applications
- Appeals to students and researchers in multiple areas of mathematics, computer science, and physics
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- About this book
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This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains.
After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions.
Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
- About the authors
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Stephen Melczer is an Assistant Professor in the Department of Combinatorics and Optimization at the University of Waterloo. Prior to joining Waterloo, he was a CRM-ISM postdoctoral fellow at the Université du Québec à Montréal, a postdoctoral fellow at the University of Pennsylvania, and a visiting scholar at the University of Illinois Urbana-Champaign. His research adapts methods from algebraic and differential geometry, analysis, and topology to create effective tools for combinatorics, mathematics, and computer science. He received doctorates from the École normale supérieure de Lyon and the University of Waterloo in 2017, and is a recipient of a Governor General Silver Academic Medal.
- Table of contents (11 chapters)
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Introduction
Pages 1-18
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Generating Functions and Analytic Combinatorics
Pages 21-91
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Multivariate Series and Diagonals
Pages 93-141
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Lattice Path Enumeration, The Kernel Method, and Diagonals
Pages 143-181
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The Theory of ACSV for Smooth Points
Pages 185-246
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Table of contents (11 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- An Invitation to Analytic Combinatorics
- Book Subtitle
- From One to Several Variables
- Authors
-
- Stephen Melczer
- Series Title
- Texts & Monographs in Symbolic Computation
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-67080-1
- DOI
- 10.1007/978-3-030-67080-1
- Hardcover ISBN
- 978-3-030-67079-5
- Series ISSN
- 0943-853X
- Edition Number
- 1
- Number of Pages
- XVIII, 418
- Number of Illustrations
- 9 b/w illustrations, 36 illustrations in colour
- Topics
