Concepts5

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.

#partition function#integer partitions#euler pentagonal theorem+11

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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 the first kind#unsigned cycle numbers#signed stirling numbers+12

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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.

#stirling numbers of the second kind#set partitions#bell numbers+12

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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.

#pollard's rho#integer factorization#cycle detection+10

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Linear Recurrence

A linear recurrence defines each term as a fixed linear combination of a small, fixed number of previous terms.

#linear recurrence#matrix exponentiation#kitamasa+12