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Enumerative Combinatorics. Volume 2 /

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Bibliographic Details
Corporate Author: ProQuest (Firm)
Other Authors: Stanley, Richard P., Fomin, Sergey
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 1999.
Series:Cambridge studies in advanced mathematics ; no. 62.
Subjects:
Combinatorial enumeration problems.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Title
  • Copyright
  • Contents
  • Foreword
  • Preface
  • Notation
  • 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.