An invitation to analytic combinatorics in several variables : from one to several variables / Stephen Melczer.
Melczer, Stephen, author.
2021
QA164
Available Online

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Title An invitation to analytic combinatorics in several variables : from one to several variables / Stephen Melczer.
Author Melczer, Stephen, author.
ISBN 9783030670801 (electronic bk.)
3030670805 (electronic bk.)
3030670791
9783030670795
DOI https://doi.org/10.1007/978-3-030-67080-1
Published Cham : Springer, [2021]
Language English
Description 1 online resource (426 pages)
Item Number 10.1007/978-3-030-67080-1 doi
Call Number QA164
Dewey Decimal Classification 511/.6
Summary 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Texts and monographs in symbolic computation.
Available in Other Form Algorithmic and Symbolic Combinatorics.
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Record Appears in Online Resources > Ebooks
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Introduction
Background and Motivation
Smooth ACSV and Applications
Non-Smooth ACSV.

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