ENUMERATIVE COMBINATORICS, volume 2
Table of Contents

• 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

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