计数组合学

Notation
Chapter 1 What Is Enumerative Combinatorics?
1.1 How to Count
1.2 Sets and Multisets
1.3 Permutation Statistics
1.4 The Twelvefold Way
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Notation
Chapter 1 What Is Enumerative Combinatorics?
1.1 How to Count
1.2 Sets and Multisets
1.3 Permutation Statistics
1.4 The Twelvefold Way
Notes
References
A Note about the Exercises
Exercises
Solutions to Exercises
Chapter 2 Sieve Methods
2.1 Inclusion-Exclusion
2.2 Examples and Special Cases
2.3 Permutations with Restricted Positions
2.4 Ferrers Boards
2.5 V-partitions and Unimodal Sequences
2.6 Involutions
2.7 Determinants
Notes
References
Exercises
Solutions to Exercises
Chapter 3 Partially Ordered Sets
3.1 Basic Concepts
3.2 New Posets from Old
3.3 Lattices
3.4 Distributive Lattices
315 Chains in Distributive Lattices
3.6 The Incidence Algebra of a Locally Finite Poset
3.7 The MObius Inversion Formula
3.8 Techniques for Computing MObius Functions
3.9 Lattices and Their MObius Algebras
3.10 The MObius Function of a Semimodular Lattice
3.11 Zeta Polynomials
3.12 Rank-selection
3.13 R-labelings
3.14 Eulerian Posets
3.15 Binomial Posets and Generating Functions
3.16 An Application to Permutation Enumeration
Notes
References
Exercises
Solutions to Exercises
Chapter 4 Rational Generating Functions
4.1 Rational Power Series in One Variable
4.2 Further Ramifications
4.3 Polynomials
4.4 Quasi-polynomials
4.5 P-partitions
4.6 Linear Homogeneous Diophantine Equations
4.7 The Transfer-matrix Method
Notes
References
Exercises
Solutions to Exercises
Appendix Graph Theory Terminology
Index
Supplementary Problems
Errata and Addenda
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