By name: combinatorics description: Counting and arrangement mathematics license: MIT compatibility: opencode metadata: audience: mathematicians category: mathematics
What I do
- Calculate permutations and combinations
- Apply binomial coefficients and Pascal's triangle
- Solve recurrence relations
- Count using inclusion-exclusion principle
- Generate combinatorial identities
- Apply generating functions
When to use me
When counting possibilities, analyzing algorithms, or solving probability problems.
Key Concepts
- Permutations: P(n,r) = n!/(n-r)! for ordered arrangements
- Combinations: C(n,r) = n!/(r!(n-r)!) for unordered selections
- Binomial Theorem: (x+y)^n = Σ C(n,k)x^{n-k}y^k
- Pigeonhole Principle: If n items into m boxes and n > m, some box has ≥2
- Recurrence Relations: a_n = f(a_{n-1}, a_{n-2}, ...) with initial conditions
- Generating Functions: G(x) = Σ a_n x^n encodes sequences