Enumerative Combinatorics: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 62)

Stanley, Richard

ISBN 10: 0521789877 / ISBN 13: 9780521789875

Published by Cambridge University Press, 2010

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Bibliographic Details

• Title: Enumerative Combinatorics: Volume 2 (Cambridge Studies in Advanced Mathematics, Series Number 62)
• Publisher: Cambridge University Press
• Publication Date: 2010
• Language: English
• ISBN 10: 0521789877
• ISBN 13: 9780521789875
• Binding: Paperback
• Condition: Used; Very Good

About this title

Synopsis

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, 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 on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

Book Description

This is the second volume of a two-volume work on the subject of enumerative combinatorics, an area of mathematics with connections to many other topics within and outside of mathematics, such as computer science, spectroscopy, algebraic geometry, algebraic topology, and representation theory. Many topics covered (in particular, the theory of symmetric functions) are not available in any other textbook at this level, and the usefulness of the book is enhanced by over 250 exercises with solutions.Although primarily intended as a textbook for graduate students and a resource for professional mathematicians, some parts of the book will be accessible to mathematics undergraduates and even interested amateurs.