Combinatorics

  1. Generating Functions
    1. Ordinary Generating Functions
      1. Definition and Construction
        1. Basic Examples
          1. Operations on Generating Functions
            1. Addition and Subtraction
              1. Multiplication
                1. Shifting Operations
                  1. Scaling Operations
                    1. Differentiation and Integration
                    2. Key Generating Function Identities
                      1. Solving Recurrence Relations
                        1. Applications to Partition Problems
                          1. Applications to Coin Change Problems
                          2. Exponential Generating Functions
                            1. Definition and Construction
                              1. Relationship to Ordinary Generating Functions
                                1. Operations on EGFs
                                  1. Applications to Labeled Structures
                                    1. Solving Recurrence Relations with EGFs
                                      1. Permutation and Arrangement Problems
                                      2. Advanced Topics
                                        1. Formal Power Series
                                          1. Coefficient Extraction
                                            1. Asymptotic Analysis
                                              1. Singularity Analysis

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                                            7. Recurrence Relations

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                                            9. Special Counting Numbers and Sequences