Generating Functions
★★★★☆Undergraduate
📖Definition
Tool encoding sequences as coefficients of polynomials or power series to solve combinatorial problems
📐Formulas
OGF: G(x) = Σaₙxⁿ
EGF: E(x) = Σaₙxⁿ/n!
Fibonacci: G(x) = x/(1-x-x²)
✏️Examples
예제 1
Partition numbers
예제 2
Catalan numbers
예제 3
Stirling numbers
⚡Applications
Solving recurrences
Combinatorial identities
Probability
🔗Related Documents
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⚡Applications
#생성함수#generating#enumeration#series