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
6.
Advanced Counting Techniques
6.1.
The Principle of Inclusion-Exclusion
6.1.1.
Statement and Motivation
6.1.2.
Two Sets Case
6.1.3.
Three Sets Case
6.1.4.
General Formula for n Sets
6.1.5.
Venn Diagram Interpretation
6.1.6.
Applications
6.1.6.1.
Counting Surjective Functions
6.1.6.2.
Derangement Problems
6.1.6.3.
Elements with Multiple Properties
6.1.6.4.
Euler's Totient Function
6.2.
The Pigeonhole Principle
6.2.1.
Simple Pigeonhole Principle
6.2.2.
Generalized Pigeonhole Principle
6.2.3.
Strong Form of Pigeonhole Principle
6.2.4.
Applications
6.2.4.1.
Existence Proofs
6.2.4.2.
Bounds and Extremal Arguments
6.2.4.3.
Number Theory Applications
6.2.4.4.
Geometric Applications
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5. The Binomial Theorem
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7. Recurrence Relations