What is included with this book?
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 | p. 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 |
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