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 …
Cross-correlation via ordinary convolution: reverse-A and reverse-B extraction methods, derivation, and Ring Trick II (cyclic shift score maximisation via difference 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.
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 …
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, …
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.
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 …
Hockey Stick identity, addition/multiplication principles, binomial identities, example problems: bitonic sequences, multiset permutations, multi-layer coloring DP, CCPC Subpermutation.
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.
A compact toolkit of geometric sums, floor-sum transformations, XOR facts, Fibonacci identities, and perfect-square patterns.
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。
Inclusion-exclusion in set and operator form, equal-count subproblems, bounded Diophantine counting, derangements, Stirling numbers, and selected contest problems.