| 书目名称 | Lessons in Enumerative Combinatorics |
| 编辑 | Ömer Eğecioğlu,Adriano M. Garsia |
| 视频video | |
| 概述 | Offers a unified and friendly approach to enumerative combinatorics through formal languages.Showcases the authors‘ unique perspective and insightful examples.Illuminates the important connection betw |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | .This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science...Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and |
| 出版日期 | Textbook 2021 |
| 关键词 | Combinatorics; bijective proofs; generating functions; planar trees; Cayley trees; Lagrange Inversion; Inc |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-71250-1 |
| isbn_softcover | 978-3-030-71252-5 |
| isbn_ebook | 978-3-030-71250-1Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer Nature Switzerland AG 2021 |
发表于 2025-3-21 20:01:16
