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Enumerative Combinatorics: Volume 2 [Kietas viršelis]

(Massachusetts Institute of Technology), Appendix by
  • Formatas: Hardback, 600 pages, aukštis x plotis x storis: 237x160x38 mm, weight: 1045 g
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 13-Jan-1999
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521560691
  • ISBN-13: 9780521560696
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 600 pages, aukštis x plotis x storis: 237x160x38 mm, weight: 1045 g
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 13-Jan-1999
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521560691
  • ISBN-13: 9780521560696
Kitos knygos pagal šią temą:
An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

Recenzijos

'This magnificent two-volume work is best described by a quote from Gian-Carlo Rota's Forward to Volume 2: I find it impossible to predict when Richard Stanley's two-volume exposition of combinatorics may be superseded. No one will dare try, let alone be able, to match the thoroughness of coverage, the care for detail, the definitiveness of proof, the elegance of presentation.' J. E. Graver 'As a researcher, Stanley has few peers in combinatorics; as at once, to pack every page with information, connect with the reader's intuition, and communicate the underlying, unifying philosophy of the subject.' D. V. Feldman, University of New Hampshire 'What else is to be added to our comments on this excellent book? Perhaps a quotation from G.-C. Rota's foreword: 'Every once in a long while, a textbook worthy of the name comes along Weber, Bertini, van der Waerden, Feller, Dunford and Schwartz, Ahlfors, Stanley.' European Mathematical Society ' an authoritative account of enumerative combinatorics.' George E. Andrews, Bulletin of the London Mathematical Society 'What else can be added to the comments upon this excellent book?' EMS Newsletter

Daugiau informacijos

An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.
Foreword v
Preface vii
Notation xi
Trees and the Composition of Generating Functions
1(158)
The Exponential Formula
1(9)
Applications of the Exponential Formula
10(12)
Enumeration of Trees
22(14)
The Lagrange Inversion Formula
36(8)
Exponential Structures
44(10)
Oriented Trees and the Matrix-Tree Theorem
54(105)
Notes
65(4)
References
69(3)
Exercises
72(31)
Solutions to Exercises
103(56)
Algebraic, D-Finite, and Noncommutative Generating Functions
159(127)
Algebraic Generating Functions
159(9)
Examples of Algebraic Series
168(11)
Diagonals
179(8)
D-Finite Generating Functions
187(8)
Noncommutative Generating Functions
195(7)
Algebraic Formal Series
202(7)
Noncommutative Diagonals
209(77)
Notes
211(3)
References
214(3)
Exercises
217(32)
Solutions to Exercises
249(37)
Symmetric Functions
286(127)
Symmetric Functions in General
286(1)
Partitions and Their Orderings
287(2)
Monomial Symmetric Functions
289(1)
Elementary Symmetric Functions
290(4)
Complete Homogeneous Symmetric Functions
294(2)
An Involution
296(1)
Power Sum Symmetric Functions
297(4)
Specializations
301(5)
A Scalar Product
306(2)
The Combinatorial Definition of Schur Functions
308(8)
The RSK Algorithm
316(6)
Some Consequences of the RSK Algorithm
322(2)
Symmetry of the RSK Algorithm
324(7)
The Dual RSK Algorithm
331(3)
The Classical Definition of Schur Functions
334(8)
The Jacobi-Trudi Identity
342(3)
The Murnaghan-Nakayama Rule
345(4)
The Characters of the Symmetric Group
349(7)
Quasisymmetric Functions
356(9)
Plane Partitions and the RSK Algorithm
365(6)
Plane Partitions with Bounded Part Size
371(7)
Reverse Plane Partitions and the Hillman-Grassl Correspondence
378(4)
Applications to Permutation Enumeration
382(8)
Enumeration under Group Action
390(23)
Notes
396(9)
References
405(8)
A1 Knuth Equivalence, Jeu de Taquin, and the Littlewood-Richardson Rule 413(27)
A1.1 Knuth Equivalence and Greene's Theorem
413(6)
A1.2 Jeu de Taquin
419(10)
A1.3 The Littlewood-Richardson Rule
429(11)
Notes
437(1)
References
438(2)
A2 The Characters of GL(n, C) 440(121)
Exercises
450(40)
Solutions to Exercises
490(71)
Index 561(22)
Additional Errata and Addenda 583