http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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.
Richard P. Stanley, Appendix by Sergey Fomin.
Cambridge studies in advanced mathematics ; no. 62