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内容简介
本书介绍了生成函数组合、树、代数生成函数、D有限生成函数、非交换生成函数和对称函数。关于对称函数的论述只适用于研究生的入门课程并着重于组合学方面，尤其是Robinson-Schensted-Knuth算法，还讨论了对称函数与表示论之间的联系。附录(由Sergey Fomin编写)中更深入地讨论了对称函数理论，包括jeu de taquin和Littlewood-richardson规则。另外，书中包含大量习题，并附有参考答案。
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目录
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 Noneommutative 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
A 1 Knuth Equivalence, Jeu de Taquln, and the Littlewood-Richardson Rule
A 1.1 Knuth Equivalence and Greene''''s Theorem
Al.2 Jeu de Taquin
Al.3 The Littlewood-Richardson Rule
Notes
References
A 2 The Characters of GL(n, C)
Exercises
Solutions to Exercises
Index
Additional Errata and Addenda
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