Combinatorics

  1. Design Theory
    1. Block Designs
      1. Definition and Parameters
        1. Incidence Structures
          1. Balanced Incomplete Block Designs
            1. Definition and Properties
              1. Necessary Conditions
                1. Fisher's Inequality
                2. Symmetric Designs
                  1. Resolvable Designs
                  2. Steiner Systems
                    1. Definition and Notation
                      1. Steiner Triple Systems
                        1. Steiner Systems S(t,k,n)
                          1. Existence Conditions
                            1. Construction Methods
                            2. Latin Squares
                              1. Definition and Properties
                                1. Order of Latin Squares
                                  1. Orthogonal Latin Squares
                                    1. Mutually Orthogonal Latin Squares
                                      1. Applications in Experimental Design
                                        1. Euler's 36 Officers Problem
                                        2. Hadamard Matrices
                                          1. Definition and Properties
                                            1. Hadamard's Conjecture
                                              1. Construction Methods
                                                1. Applications to Coding Theory

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                                              10. Graph Theory and Combinatorics

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                                              12. Probabilistic Combinatorics