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

• Chapter 1: What is Enumerative Combinatorics?

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  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. The Möbius inversion formula
  8. Techniques for computing Möbius functions
  9. Lattices and their Möbius functions
  10. The Möbius function of a semimodular lattice
  11. Hyperplane arrangements
  12. Zeta polynomials
  13. Rank-selection
  14. R-labelings
  15. (P,ω)-partitions
  16. Eulerian posets
  17. The cd-index of an Eulerian poset
  18. Binomial posets and generating functions
  19. An application to permutation enumeration
  20. Promotion and evacuation
  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

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