https://jasper-aa64.github.io/tags/generating-function/Recent content in Generating-Function on JasperHugoen-usSat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Polynomial representations, FFT/DFT over complex numbers, Triple Sums, Fuzzy Search (difference convolution), FFT template, Lagrange interpolation (O(n²) and O(n) equidistant), sum of k-th powers, Assigning Prizes polynomial DP.https://jasper-aa64.github.io/posts/combinatorics-2-2-primitive-roots-ntt/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-2-primitive-roots-ntt/Order and primitive roots (Euler’s theorem, BSGS, exBSGS), discrete index as logarithm analogue, SGU 261 Discrete Roots, NTT theory and templates, divide-and-conquer NTT (product tree), Wannafly D team selection, Nowcoder 50F generating functions.https://jasper-aa64.github.io/posts/combinatorics-3-1-ordinary-generating-functions/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-3-1-ordinary-generating-functions/Formal power series basics, ordinary generating functions, inversion identities, generalized binomial expansions, bounded counting examples, and recurrence-to-closed-form examples such as Fibonacci and Catalan.https://jasper-aa64.github.io/posts/combinatorics-3-2-more-operations-on-formal-power-series/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-3-2-more-operations-on-formal-power-series/Newton iteration for polynomial inverse and square root, derivative/integral/composition of formal power series, logarithm and exponential of series, and worked examples including CF438E and a bad-modulus complete-knapsack generating function.