(EBOOK PDF)Enumerative Combinatorics Volume 2 2nd edition by Richard Stanley 9780511835568 0511835566 full chapters

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• ISBN 10:0511835566 

• ISBN 13:9780511835568

• Author:Richard Stanley 

 Enumerative Combinatorics: Volume 2
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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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.

Enumerative Combinatorics: Volume 2 2nd Table of contents:

5 Trees and the Composition of Generating Functions
5.1 The Exponential Formula
5.2 Applications of the Exponential Formula
5.3 Enumeration of Trees
5.4 The Lagrange Inversion Formula
5.5 Exponential Structures
5.6 Oriented Trees and the Matrix-Tree Theorem
Notes
References
Exercises
Solutions to Exercises
6 Algebraic, D-Finite, and Noncommutative Generating Functions
6.1 Algebraic Generating Functions
6.2 Examples of Algebraic Series
6.3 Diagonals
6.4 D-Finite Generating Functions
6.5 Noncommutative Generating Functions
6.6 Algebraic Formal Series
6.7 Noncommutative Diagonals
Notes
References
Exercises
Solutions to Exercises
7 Symmetric Functions
7.1 Symmetric Functions in General
7.2 Partitions and Their Orderings
7.3 Monomial Symmetric Functions
7.4 Elementary Symmetric Functions
7.5 Complete Homogeneous Symmetric Functions
7.6 An Involution
7.7 Power Sum Symmetric Functions
7.8 Specializations
7.9 A Scalar Product
7.10 The Combinatorial Definition of Schur Functions
7.11 The RSK Algorithm
7.12 Some Consequences of the RSK Algorithm
7.13 Symmetry of the RSK Algorithm
7.14 The Dual RSK Algorithm
7.15 The Classical Definition of Schur Functions
7.16 The Jacobi-Trudi Identity
7.17 The Murnaghan-Nakayama Rule
7.18 The Characters of the Symmetric Group
7.19 Quasisymmetric Functions
7.20 Plane Partitions and the RSK Algorithm
7.21 Plane Partitions with Bounded Part Size
7.22 Reverse Plane Partitions and the Hillman-Grassl Correspondence
7.23 Applications to Permutation Enumeration
7.24 Enumeration under Group Action
Notes
References
A1 Knuth Equivalence, Jeu de Taquin, and the Littlewood-Richardson Rule
A1.1 Knuth Equivalence and Greene’s Theorem
A1.2 Jeu de Taquin
Al.3 The Littlewood-Richardson Rule
Notes
References
A2 The Characters of GL(n, C)
Exercises
Solutions to Exercises
Index
Additional Errata and Addenda

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