Enumerative Combinatorics: Volume 2

Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.

Richard Stanley (Author)

9781009262484, Cambridge University Press

Paperback / softback, published 17 August 2023

788 pages
22.9 x 15.2 x 4.1 cm, 1.11 kg

'Richard Stanley's Enumerative Combinatorics, in two volumes, is an essential reference for researchers and graduate students in the field of enumeration. Volume 2, newly revised, includes comprehensive coverage of composition and inversion of generating functions, exponential and algebraic generating functions, and symmetric functions. The treatment of symmetric functions is especially noteworthy for its thoroughness and accessibility. Engaging problems and solutions, and detailed historical notes, add to the value of this book. It provides an excellent introduction to the subject for beginners while also offering advanced researchers new insights and perspectives.' Ira Gessel, Brandeis University

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.

Preface to Second Edition
Preface
5. Trees and the Composition of Generating Functions
6. Algebraic Generating Functions
7. Symmetric Functions
Appendices: References
Index.

Subject Areas: Discrete mathematics [PBD]