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An invitation to analytic combinator...

Melczer, Stephen.

An invitation to analytic combinatoricsfrom one to several variables /

Record Type:	Electronic resources : Monograph/item
Title/Author:	An invitation to analytic combinatoricsby Stephen Melczer.
Reminder of title:	from one to several variables /
remainder title:	Algorithmic and symbolic combinatorics :
Author:	Melczer, Stephen.
Published:	Cham :Springer International Publishing :2021.
Description:	xviii, 418 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Combinatorial analysis.
Online resource:	https://doi.org/10.1007/978-3-030-67080-1
ISBN:	9783030670801$q(electronic bk.)

An invitation to analytic combinatoricsfrom one to several variables /
Melczer, Stephen.

An invitation to analytic combinatoricsfrom one to several variables /[electronic resource] :Algorithmic and symbolic combinatorics :an invitation to analytic combinatorics in several variablesby Stephen Melczer. - Cham :Springer International Publishing :2021. - xviii, 418 p. :ill., digital ;24 cm. - Texts & monographs in symbolic computation. - Texts & monographs in symbolic computation..

Introduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV.

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.

ISBN: 9783030670801$q(electronic bk.)

Standard No.: 10.1007/978-3-030-67080-1doiSubjects--Topical Terms:

182280
Combinatorial analysis.

LC Class. No.: QA164

Dewey Class. No.: 511.6

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245 1 0 $a An invitation to analytic combinatorics $h [electronic resource] : $b from one to several variables / $c by Stephen Melczer.
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505 0 $a Introduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV.
520 $a 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.
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