Algorithmic and Symbolic Combinatorics:An Invitation to Analytic Combinatorics in Several Variables


An Invitation to Analytic Combinatorics:From One to Several Variables (Texts & Monographs in Symbolic Computation)
by:Stephen Melczer
Publisher Finelybook 出版社:Springer; 1st ed. 2021 edition (December 23, 2020)
Language 语言:English
pages 页数:436 pages
ISBN-10 书号:3030670791
ISBN-13 书号:9783030670795

Book Description
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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