How this calculation works
Count self-inverse permutations, whose cycles all have length one or two.
THE FORMULA
I(n)=I(n−1)+(n−1)I(n−2)A worked example
Four elements have one identity, six single swaps and three double swaps.
Good to know
Fixed points are allowed.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count self-inverse permutations, whose cycles all have length one or two.
The primary result is labeled “Involutions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Fixed points are allowed.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Four elements have one identity, six single swaps and three double swaps.
Which rule does this calculator apply?
I(n)=I(n−1)+(n−1)I(n−2)