Table of Contents

- Chapter 1: What is Enumerative Combinatorics?

- How to count
- Sets and multisets
- Permutation statistics
- The Twelvefold Way

Notes

References

Exercises

Solutions to exercises

- Chapter 2: Sieve methods
- Inclusion-exclusion
- Examples and special cases
- Permutations with restricted positions
- Ferrers boards
- V-partitions and unimodal sequences
- Involutions
- Determinants

Notes

References

Exercises

Solutions to exercises

- Chapter 3: Partially Ordered Sets
- Basic concepts
- New posets from old
- Lattices
- Distributive lattices
- Chains in distributive lattices
- The incidence algebra of a locally finite poset
- The Möbius inversion formula
- Techniques for computing Möbius functions
- Lattices and their Möbius functions
- The Möbius function of a semimodular lattice
- Zeta polynomials
- Rank-selection
- R-labelings
- Eulerian posets
- Binomial posets and generating functions
- An application to permutation enumeration

Notes

References

Exercises

Solutions to exercises

- Chapter 4: Rational generating functions
- Rational power series in one variable
- Further ramifications
- Polynomials
- Quasi-polynomials
- P-partitions
- Linear homogeneous diophantine equations
- The transfer-matrix method

Notes

References

Exercises

Solutions to exercises

Appendix: Graph Theory Terminology

Errata to the First Printing

Supplementary Exercises

Index

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