Combinatorics

  1. Recurrence Relations
    1. Introduction to Recurrence Relations
      1. Definition and Examples
        1. Initial Conditions
          1. Order of Recurrence Relations
            1. Modeling Problems with Recurrences
            2. Classic Examples
              1. Tower of Hanoi
                1. Fibonacci Numbers
                  1. Catalan Numbers
                    1. Tribonacci Numbers
                    2. Linear Homogeneous Recurrence Relations
                      1. Definition and Structure
                        1. First-Order Relations
                          1. Second-Order Relations
                            1. The Characteristic Equation
                              1. Distinct Roots Case
                                1. Repeated Roots Case
                                  1. Complex Roots Case
                                    1. General Solutions
                                    2. Linear Non-Homogeneous Recurrence Relations
                                      1. Definition and Structure
                                        1. Homogeneous and Particular Solutions
                                          1. Method of Undetermined Coefficients
                                            1. Variation of Parameters
                                              1. Superposition Principle
                                              2. Advanced Techniques
                                                1. Substitution Methods
                                                  1. Generating Function Approach
                                                    1. Matrix Methods

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                                                  6. Advanced Counting Techniques

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                                                  8. Generating Functions