ENUMERATIVE COMBINATORICS, volume 1, second edition
Table of Contents (tentative)

• Chapter 1: What is Enumerative Combinatorics?

  ---

  1. How to count
  2. Sets and multisets
  3. Cycles and inversions
  4. Descents
  5. Geometric representations of permutations
  6. Alternating permutations, Euler numbers, and the cd-index of S_n
  7. Permutations of multisets
  8. Partition identities
  9. The Twelvefold Way
  10. Two q-analogues of permutations
      Notes
      References
      Exercises
      Solutions to exercises

• Chapter 2: Sieve methods
  1. Inclusion-exclusion
  2. Examples and special cases
  3. Permutations with restricted positions
  4. Ferrers boards
  5. V-partitions and unimodal sequences
  6. Involutions
  7. Determinants
     Notes
     References
     Exercises
     Solutions to exercises

• Chapter 3: Partially Ordered Sets
  1. Basic concepts
  2. New posets from old
  3. Lattices
  4. Distributive lattices
  5. Chains in distributive lattices
  6. Incidence algebras
  7. Promotion and evacuation
  8. The Möbius inversion formula
  9. Techniques for computing Möbius functions
  10. Lattices and their Möbius functions
  11. The Möbius function of a semimodular lattice
  12. Hyperplane arrangements
  13. Zeta polynomials
  14. Rank-selection
  15. R-labelings
  16. (P,ω)-partitions
  17. Eulerian posets
  18. The cd-index of an Eulerian poset
  19. Binomial posets and generating functions
  20. An application to permutation enumeration
  21. Differential posets
      Notes
      References
      Exercises
      Solutions to exercises

• Chapter 4: Rational generating functions
  1. Rational power series in one variable
  2. Further ramifications
  3. Polynomials
  4. Quasipolynomials
  5. Linear homogeneous diophantine equations
  6. Applications
  7. The transfer-matrix method
     Notes
     References
     Exercises
     Solutions to exercises
  
  Appendix: Graph Theory Terminology
  Index

Richard Stanley's Home Page