ENUMERATIVE COMBINATORICS, volume 1
Table of Contents

• Chapter 1: What is Enumerative Combinatorics?

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  1. How to count
  2. Sets and multisets
  3. Permutation statistics
  4. The Twelvefold Way
     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. The incidence algebra of a locally finite poset
  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. Zeta polynomials
  12. Rank-selection
  13. R-labelings
  14. Eulerian posets
  15. Binomial posets and generating functions
  16. An application to permutation enumeration
      Notes
      References
      Exercises
      Solutions to exercises

• Chapter 4: Rational generating functions
  1. Rational power series in one variable
  2. Further ramifications
  3. Polynomials
  4. Quasi-polynomials
  5. P-partitions
  6. Linear homogeneous diophantine equations
  7. 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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