Enumerative Combinatorics

Volume 2

Richard Stanley (Massachusetts Institute of Technology)

$242.95

Hardback

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English

Cambridge University Press
17 August 2023

Discrete mathematics; Algebra; Combinatorics & graph theory; Maths for computer scientists

Series: Cambridge Studies in Advanced Mathematics

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.

By: Richard Stanley (Massachusetts Institute of Technology)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 235mm, Width: 156mm, Spine: 46mm
Weight: 1.230kg
ISBN: 9781009262491
ISBN 10: 1009262491
Series: Cambridge Studies in Advanced Mathematics
Pages: 788
Publication Date: 17 August 2023
Audience: College/higher education , A / AS level
Format: Hardback
Publisher's Status: Active

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

Richard P. Stanley is Emeritus Professor of Mathematics at the Massachusetts Institute of Technology and an Arts and Sciences Distinguished Professor at the University of Miami. He has written over 180 research articles and six books. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995) and the 2001 Leroy P. Steele Prize for Mathematical Exposition.

Reviews for Enumerative Combinatorics: Volume 2

'I have used Richard Stanley's books on Enumerative Combinatorics numerous times for the combinatorics classes I have taught. This new edition contains many new exercises, which will no doubt be extremely useful for the next generation of combinatorialists.' Anne Schilling, University of California, Davis 'This is one of the great books; readable, deep and full of gems. It brings algebraic combinatorics to life. I teach out of it and feel that if I can get my students to 'touch Stanley' I have given them a gift for life.' Persi Diaconis, Stanford University 'It is wonderful to celebrate the completion of the second edition of Richard Stanley's Enumerative Combinatorics, one of the finest mathematical works of all time. He has added nearly 200 exercises, together with their answers, to what was already a uniquely masterful summary of a vast and beautiful theory. When paired with the second edition of Volume 1, his two classic volumes will surely be a timeless treasure for generations to come.' Donald E. Knuth, Stanford University