https://jasper-aa64.github.io/categories/combinatorics/Recent content in Combinatorics on JasperHugoen-usSun, 26 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-order-theory/Sun, 26 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-order-theory/Chromatic polynomial, chordal/interval graphs, PEO product formula, order polynomials (chain/antichain/tree/DAG/divisor lattice), MacMahon formula, Dilworth, Mirsky, Hall’s marriage theorem, Erdős–Szekeres, missile interception.https://jasper-aa64.github.io/posts/combinatorics-2-ex1-difference-convolution/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-ex1-difference-convolution/Cross-correlation via ordinary convolution: reverse-A and reverse-B extraction methods, derivation, and Ring Trick II (cyclic shift score maximisation via difference convolution).https://jasper-aa64.github.io/posts/combinatorics-2-ex2-cyclic-convolution/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-ex2-cyclic-convolution/Cyclic convolution definition, FFT/NTT implementation for n=2^k, zero-padding, why n must be a power of two, and the fold-back technique for arbitrary n.https://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.https://jasper-aa64.github.io/posts/combinatorics-1-1-permutations-combinations/Fri, 24 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-1-1-permutations-combinations/Hockey Stick identity, addition/multiplication principles, binomial identities, example problems: bitonic sequences, multiset permutations, multi-layer coloring DP, CCPC Subpermutation.https://jasper-aa64.github.io/posts/combinatorics-d1-diophantine-equations/Fri, 24 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-d1-diophantine-equations/Stars and bars, bounded Diophantine equations via inclusion-exclusion, prefix-sum DP, D&C NTT, equal-cap formula, and a full worked example on CF 2127F.https://jasper-aa64.github.io/posts/combinatorics-0-common-formulae-conclusions/Mon, 20 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-0-common-formulae-conclusions/A compact toolkit of geometric sums, floor-sum transformations, XOR facts, Fibonacci identities, and perfect-square patterns.https://jasper-aa64.github.io/posts/combinatorics-1-counting-conclusions/Mon, 20 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-1-counting-conclusions/常见计数结论、Lucas 定理、不定方程解计数、平面分拆、DAG 路径计数、多项式平移、XOR 均匀性与若干竞赛常用结论。https://jasper-aa64.github.io/posts/combinatorics-1-2-inclusion-exclusion-diophantine-derangements/Mon, 20 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-1-2-inclusion-exclusion-diophantine-derangements/Inclusion-exclusion in set and operator form, equal-count subproblems, bounded Diophantine counting, derangements, Stirling numbers, and selected contest problems.https://jasper-aa64.github.io/posts/combinatorics-1-2-cn/Mon, 20 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-1-2-cn/容斥原理的集合与算子形式、有上下界不定方程计数（前缀和DP与分治NTT）、错排公式与第二类斯特林数。