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商品詳細
An Invitation to Analytic Combinatorics : From One to Several Variables. 1st ed. 2021.
・ISBN 978-3-030-67082-5 paper EUR 139.99
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| 著者・編者 | Melczer, Stephen, |
|---|---|
| シリーズ | Texts & Monographs in Symbolic Computation |
| 出版社 | (Springer Nature Switzerland AG, SZ) |
| 出版年月 | 2021 |
| ページ数 | 418 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-5964＞ |
解説
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 theorycan 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.