Concepts7
Partition Function
The partition function p(n) counts the number of ways to write n as a sum of positive integers where order does not matter.
Stirling Numbers of First Kind
Stirling numbers of the first kind count permutations by their number of cycles and connect power polynomials to rising/falling factorials.
Stirling Numbers of Second Kind
Stirling numbers of the second kind S(n,k) count how many ways to split n labeled items into k non-empty, unlabeled groups.
Pollard's Rho Factorization
Pollard's Rho is a randomized algorithm that finds a non-trivial factor of a composite integer by walking a pseudorandom sequence modulo n and extracting a factor with a gcd.
NTT (Number Theoretic Transform)
The Number Theoretic Transform (NTT) is an FFT-like algorithm that performs discrete convolutions exactly using modular arithmetic instead of floating-point numbers.
Linear Recurrence
A linear recurrence defines each term as a fixed linear combination of a small, fixed number of previous terms.
Aho-Corasick - DP Applications
Aho–Corasick (AC) turns a set of forbidden patterns into a finite automaton that lets you process or generate strings while tracking whether any pattern appears.