Concepts3
∑MathAdvanced
Generating Functions - EGF
Exponential generating functions (EGFs) encode a sequence (a_n) as A(x) = \sum_{n \ge 0} a_n \frac{x^n}{n!}, which naturally models labeled combinatorial objects.
#exponential generating function#egf#binomial convolution+11
∑MathAdvanced
Generating Functions - OGF
An ordinary generating function (OGF) encodes a sequence (a_n) as a formal power series A(x) = \sum_{n \ge 0} a_n x^n.
#ordinary generating function#ogf#coefficient extraction+12
⚙️AlgorithmAdvanced
Polynomial Operations
Fast polynomial operations treat coefficients like numbers but use FFT/NTT to multiply in O(n \log n) time instead of O(n^2).
#polynomial#ntt#fft+12