You are here

Enumerative Combinatorics Vol. II

Richard P. Stanley
Publisher: 
Cambridge University Press
Publication Date: 
2001
Number of Pages: 
585
Format: 
Paperback
Series: 
Cambridge Studies in Advanced Mathematics 62
Price: 
55.00
ISBN: 
9780521789875.
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on
08/9/2013
]

About a year and a half ago, Darren Glass wrote a glowing review of the second edition of Volume 1 of Enumerative Combinatorics. Both volumes already had pages on MAA Reviews, because both appeared in the MAA's Basic Library List with the strongest possible recommendation: "The Basic Library List Committee considers this book essential for undergraduate mathematics libraries." At the time, I put off doing a review of the second volume because I assumed that it too would receive a second edition. This must have been a common assumption, because one now finds a note on Stanley's web site indicating that "there will be no second edition of Volume 2." The point is that Volume 1, originally published in 1986, needed spiffing up, while Volume 2, born in 1999, does not.

Given that, let me just point you to our review of volume 1 and add only that this is the real thing, a book universally considered the gold standard in its field. Anyone interested in combinatorics is going to need to have both volumes on their shelves.


Fernando Q. Gouvêa is the editor of MAA Reviews.

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

Dummy View - NOT TO BE DELETED