Foreword: v
Preface: vii
Notation: xi
• Chapter 5: Trees and the Composition of Generating Functions

1. The exponential formula: 1
2. Applications of the exponential formula: 10
3. Enumeration of trees: 22
4. The Lagrange inversion formula: 36
5. Exponential structures: 44
6. Oriented trees and the Matrix-Tree Theorem: 54
Notes: 65
References: 69
Exercises: 72
Solutions to exercises: 103

• Chapter 6: Algebraic, D-Finite, and Noncommutative Generating Functions

1. Algebraic generating functions: 159
2. Examples of algebraic series: 168
3. Diagonals: 179
4. D-finite generating functions: 187
5. Noncommutative generating functions: 195
6. Algebraic formal series: 202
7. Noncommutative diagonals: 209
Notes: 211
References: 214
Exercises: 217
Solutions to exercises: 249

• Chapter 7: Symmetric functions

1. Symmetric functions in general: 286
2. Partitions and their orderings: 287
3. Monomial symmetric functions: 289
4. Elementary symmetric functions: 290
5. Complete homogeneous symmetric functions: 294
6. An involution: 296
7. Power sum symmetric functions: 297
8. Specializations: 301
9. A scalar product: 306
10. The combinatorial definition of Schur functions: 308
11. The RSK-algorithm: 316
12. Some consequences of the RSK-algorithm: 322
13. Symmetry of the RSK-algorithm: 324
14. The dual RSK-algorithm: 331
15. The classical definition of Schur functions: 334
16. The Jacobi-Trudi identity: 342
17. The Murnaghan-Nakayama rule: 345
18. The characters of the symmetric group: 349
19. Quasisymmetric functions: 356
20. Plane partitions and the RSK-algorithm: 365
21. Plane partitions with bounded part size: 371
22. Reverse plane partitions and the Hillman-Grassl correspondence: 378
23. Applications to permutation enumeration: 382
24. Enumeration under group action: 390
Notes: 396
References: 405
Appendix on Knuth equivalence, jeu de taquin, and the Littlewood-Richardson rule (by Sergey Fomin): 413
Appendix on The characters of GL(n,C): 440
Exercises: 450
Solutions to exercises: 490

Index: 561