Enumerative Combinatorics: Volume 1
ISBN: 9781107602625 | 1107602629
Edition: 2ndFormat: Paperback
Publisher: Cambridge Univ Pr
Pub. Date: 1/31/2012
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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 more than 300 new exercises, many with solutions, updated and expanded chapter bibliographies and substantial new material on permutation statistics.
This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises.
This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises.
| Preface | p. xi |
| Acknowledgments | p. xiii |
| What Is Enumerative Combinatorics? | p. 1 |
| How to Count | p. 1 |
| Sets and Multisets | p. 15 |
| Cycles and Inversions | p. 22 |
| Descents | p. 31 |
| Geometric Representations of Permutations | p. 41 |
| Alternating Permutations, Euler Numbers, and the cd-lndex of $$$n | p. 46 |
| Permutations of Multisets | ... MOREp. 54 |
| Partition Identities | p. 61 |
| The Twelvefold Way | p. 71 |
| Two q-Analogues of Permutations | p. 80 |
| Notes | p. 97 |
| Bibliography | p. 100 |
| Exercises for Chapter 1 | p. 103 |
| Solutions to Exercises | p. 141 |
| Sieve Methods | p. 195 |
| Inclusion-Exclusion | p. 195 |
| Examples and Special Cases | p. 198 |
| Permutations with Restricted Position | p. 202 |
| Ferrers Boards | p. 207 |
| V-Partitions and Unimodal Sequences | p. 209 |
| Involutions | p. 212 |
| Determinants | p. 215 |
| Notes | p. 218 |
| Bibliography | p. 219 |
| Exercises for Chapter 2 | p. 220 |
| Solutions to Exercises | p. 231 |
| Partially Ordered Sets | p. 241 |
| Basic Concepts | p. 241 |
| New Posets from Old | p. 246 |
| Lattices | p. 248 |
| Distributive Lattices | p. 252 |
| Chains in Distributive Lattices | p. 256 |
| Incidence Algebras | p. 261 |
| The Möbius Inversion Formula | p. 264 |
| Techniques for Computing Möbius Functions | p. 266 |
| Lattices and Their Möbius Functions | p. 274 |
| The Mobius Function of a Semimodular Lattice | p. 277 |
| Hyperplane Arrangements | p. 280 |
| Zeta Polynomials | p. 291 |
| Rank Selection | p. 293 |
| R-Labelings | p. 295 |
| (P,¿)-Partitions | p. 298 |
| Eulerian Posets | p. 310 |
| The cd-Index of an Eulerian Poset | p. 315 |
| Binomial Posets and Generating Functions | p. 320 |
| An Application to Permutation Enumeration | p. 327 |
| Promotion and Evacuation | p. 330 |
| Differential Posets | p. 334 |
| Notes | p. 345 |
| Bibliography | p. 349 |
| Exercises for Chapter 3 | p. 353 |
| Solutions to Exercises | p. 408 |
| Rational Generating Functions | p. 464 |
| Rational Power Series in One Variable | p. 464 |
| Further Ramifications | p. 467 |
| Polynomials | p. 471 |
| Quasipolynomials | p. 474 |
| Linear Homogeneous Diophantine Equations | p. 475 |
| Applications | p. 488 |
| The Transfer-Matrix Method | p. 500 |
| Notes | p. 523 |
| Bibliography | p. 526 |
| Exercises for Chapter 4 | p. 528 |
| Solutions to Exercises | p. 548 |
| Appendix: Graph Theory Terminology | p. 571 |
| First Edition Numbering | p. 575 |
| List of Notation (Partial) | p. 581 |
| Index | p. 585 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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.
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