An invitation to analytic combinatorics in several variables : from one to several variables / Stephen Melczer.

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An invitation to analytic combinatorics in several variables : from one to several variables / Stephen Melczer.

9783030670801 (electronic bk.)
3030670805 (electronic bk.)
3030670791
9783030670795

Cham : Springer, [2021]

English

1 online resource (426 pages).

10.1007/978-3-030-67080-1 doi

QA164

511/.6

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.

Includes bibliographical references.

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Description based on print version record.

Texts and monographs in symbolic computation.

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