How this calculation works
Count permutations with exactly k disjoint cycles.
THE FORMULA
c(n,k)=c(n−1,k−1)+(n−1)c(n−1,k)A worked example
Four elements admit eleven permutations with two cycles.
Good to know
The result is the unsigned Stirling number of the first kind.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count permutations with exactly k disjoint cycles.
The primary result is labeled “Permutations”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The result is the unsigned Stirling number of the first kind.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Four elements admit eleven permutations with two cycles.
Which rule does this calculator apply?
c(n,k)=c(n−1,k−1)+(n−1)c(n−1,k)