Combinatorics

  1. Permutations
    1. Arrangements of Distinct Objects
      1. Definition of Permutation
        1. Full Permutations
          1. Partial Permutations
            1. The Formula P(n,k)
              1. Relationship to Factorials
              2. Permutations with Repetition
                1. Definition and Examples
                  1. Multinomial Coefficients
                    1. Multinomial Formula
                      1. Applications to Word Arrangements
                      2. Circular Permutations
                        1. Definition and Properties
                          1. Linear vs. Circular Arrangements
                            1. Formula for Circular Permutations
                              1. Rotational Symmetry
                                1. Necklace Problems
                                2. Derangements
                                  1. Definition and Motivation
                                    1. Basic Examples
                                      1. The Subfactorial Notation
                                        1. Recurrence Relation for Derangements
                                          1. Inclusion-Exclusion Formula
                                            1. Asymptotic Behavior
                                              1. Applications of Derangements

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                                            2. Fundamental Counting Principles

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                                            4. Combinations