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EC1 Contents

  • Chapter 1: What is Enumerative Combinatorics?
    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