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
3.
Permutations
3.1.
Arrangements of Distinct Objects
3.1.1.
Definition of Permutation
3.1.2.
Full Permutations
3.1.3.
Partial Permutations
3.1.4.
The Formula P(n,k)
3.1.5.
Relationship to Factorials
3.2.
Permutations with Repetition
3.2.1.
Definition and Examples
3.2.2.
Multinomial Coefficients
3.2.3.
Multinomial Formula
3.2.4.
Applications to Word Arrangements
3.3.
Circular Permutations
3.3.1.
Definition and Properties
3.3.2.
Linear vs. Circular Arrangements
3.3.3.
Formula for Circular Permutations
3.3.4.
Rotational Symmetry
3.3.5.
Necklace Problems
3.4.
Derangements
3.4.1.
Definition and Motivation
3.4.2.
Basic Examples
3.4.3.
The Subfactorial Notation
3.4.4.
Recurrence Relation for Derangements
3.4.5.
Inclusion-Exclusion Formula
3.4.6.
Asymptotic Behavior
3.4.7.
Applications of Derangements
Previous
2. Fundamental Counting Principles
Go to top
Next
4. Combinations