Cambridge University Press eBooks· 2023· Book chapter
Enumerative Combinatorics
- 274citations
- 2023year
Short summary
The revised second edition of Stanley's Volume II provides a comprehensive introduction to generating functions, trees, and symmetric functions, featuring over 400 exercises with solutions.
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Key points
- Covers generating functions (exponential, Lagrange inversion), trees, and symmetric functions.
- Includes a unique introductory graduate-level treatment of symmetric functions and the Robinson–Schensted–Knuth algorithm.
- Features an appendix by Sergey Fomin on jeu de taquin and the Littlewood–Richardson rule.
- Contains over 400 exercises, with 159 new exercises on symmetric functions, all with solutions or references.
AI-generated from the title and abstract; the full text is not read.
Abstract
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2023 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics