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 1 Principles of Combinatorics
  1.1 Typical counting questions and the product principle
  1.2 Counting, overcounting, and the sum principle
  1.3 Functions and the bijection principle
  1.4 Relations and the equivalence principle
  1.5 Existence and the pigeonhole principle
 2 Distributions and Combinatorial Proofs
  2.1 Counting functions
  2.2 Counting subsets and multisets
  2.3 Counting set partitions
  2.4 Counting integer partitions
 3 Algebraic Tools
  3.1 Inclusion-exclusion
  3.2 Mathematical induction
  3.3 Using generating functions, part I
  3.4 Using generating functions, part II
  3.5 Techniques for solving recurrence relations
  3.6 Solving linear recurrence relations
 4 Famous Number Families
  4.1 Binomial and multinomial coefficients
  4.2 Fibonacci and Lucas numbers
  4.3 Stirling numbers
  4.4 Integer partition numbers
 5 Counting Under Equivalence
  5.1 Two examples
  5.2 Permutation groups
  5.3 Orbits and fixed point sets
  5.4 Using the CFB theorem
  5.5 Proving the CFB theorem
  5.6 The cycle index and Pólya's theorem
 6 Combinatorics on Graphs
  6.1 Basic graph theory
  6.2 Counting trees
  6.3 Coloring and the chromatic polynomial
  6.4 Ramsey theory
 7 Designs and Codes
  7.1 Construction methods for designs
  7.2 The incidence matrix and symmetric designs
  7.3 Fisher's inequality and Steiner systems
  7.4 Perfect binary codes
  7.5 Codes from designs, designs from codes
 8 Partially Ordered Sets
  8.1 Poset examples and vocabulary
  8.2 Isomorphism and Sperner's theorem
  8.3 Dilworth's theorem
  8.4 Dimension
  8.5 Möbius inversion, part I
  8.6 Möbius inversion, part II
 Bibliography
 Hints and Answers to Selected Exercises
 List of Notation
 Index
 About the Author