UsefulLinks
Mathematics
Combinatorics
1. Introduction to Combinatorics
2. Fundamental Counting Principles
3. Permutations
4. Combinations
5. The Binomial Theorem
6. Advanced Counting Techniques
7. Recurrence Relations
8. Generating Functions
9. Special Counting Numbers and Sequences
10. Graph Theory and Combinatorics
11. Design Theory
12. Probabilistic Combinatorics
13. Algebraic Combinatorics
14. Extremal Combinatorics
15. Applications and Advanced Topics
8.
Generating Functions
8.1.
Ordinary Generating Functions
8.1.1.
Definition and Construction
8.1.2.
Basic Examples
8.1.3.
Operations on Generating Functions
8.1.3.1.
Addition and Subtraction
8.1.3.2.
Multiplication
8.1.3.3.
Shifting Operations
8.1.3.4.
Scaling Operations
8.1.3.5.
Differentiation and Integration
8.1.4.
Key Generating Function Identities
8.1.5.
Solving Recurrence Relations
8.1.6.
Applications to Partition Problems
8.1.7.
Applications to Coin Change Problems
8.2.
Exponential Generating Functions
8.2.1.
Definition and Construction
8.2.2.
Relationship to Ordinary Generating Functions
8.2.3.
Operations on EGFs
8.2.4.
Applications to Labeled Structures
8.2.5.
Solving Recurrence Relations with EGFs
8.2.6.
Permutation and Arrangement Problems
8.3.
Advanced Topics
8.3.1.
Formal Power Series
8.3.2.
Coefficient Extraction
8.3.3.
Asymptotic Analysis
8.3.4.
Singularity Analysis
Previous
7. Recurrence Relations
Go to top
Next
9. Special Counting Numbers and Sequences