Enumerative Combinatorics

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2011-12-12
  • Publisher: Cambridge Univ Pr
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Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Author Biography

Richard P. Stanley is a professor of applied mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. In addition to the seminal two-volume book Enumerative Combinatories, he is the author of Combinatories and Commutative Algebra (1983) and more than 100 research articles in National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition, and the 2003 Schock Prize.

Table of Contents

Prefacep. xi
Acknowledgmentsp. xiii
What Is Enumerative Combinatorics?p. 1
How to Countp. 1
Sets and Multisetsp. 15
Cycles and Inversionsp. 22
Descentsp. 31
Geometric Representations of Permutationsp. 41
Alternating Permutations, Euler Numbers, and the cd-lndex of $$$np. 46
Permutations of Multisetsp. 54
Partition Identitiesp. 61
The Twelvefold Wayp. 71
Two q-Analogues of Permutationsp. 80
Notesp. 97
Bibliographyp. 100
Exercises for Chapter 1p. 103
Solutions to Exercisesp. 141
Sieve Methodsp. 195
Inclusion-Exclusionp. 195
Examples and Special Casesp. 198
Permutations with Restricted Positionp. 202
Ferrers Boardsp. 207
V-Partitions and Unimodal Sequencesp. 209
Involutionsp. 212
Determinantsp. 215
Notesp. 218
Bibliographyp. 219
Exercises for Chapter 2p. 220
Solutions to Exercisesp. 231
Partially Ordered Setsp. 241
Basic Conceptsp. 241
New Posets from Oldp. 246
Latticesp. 248
Distributive Latticesp. 252
Chains in Distributive Latticesp. 256
Incidence Algebrasp. 261
The Möbius Inversion Formulap. 264
Techniques for Computing Möbius Functionsp. 266
Lattices and Their Möbius Functionsp. 274
The Mobius Function of a Semimodular Latticep. 277
Hyperplane Arrangementsp. 280
Zeta Polynomialsp. 291
Rank Selectionp. 293
R-Labelingsp. 295
(P,¿)-Partitionsp. 298
Eulerian Posetsp. 310
The cd-Index of an Eulerian Posetp. 315
Binomial Posets and Generating Functionsp. 320
An Application to Permutation Enumerationp. 327
Promotion and Evacuationp. 330
Differential Posetsp. 334
Notesp. 345
Bibliographyp. 349
Exercises for Chapter 3p. 353
Solutions to Exercisesp. 408
Rational Generating Functionsp. 464
Rational Power Series in One Variablep. 464
Further Ramificationsp. 467
Polynomialsp. 471
Quasipolynomialsp. 474
Linear Homogeneous Diophantine Equationsp. 475
Applicationsp. 488
The Transfer-Matrix Methodp. 500
Notesp. 523
Bibliographyp. 526
Exercises for Chapter 4p. 528
Solutions to Exercisesp. 548
Appendix: Graph Theory Terminologyp. 571
First Edition Numberingp. 575
List of Notation (Partial)p. 581
Indexp. 585
Table of Contents provided by Ingram. All Rights Reserved.

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