- The product of a permutation with its inverse gives the identity permutation.
- Every permutation has a uniquely defined inverse.
- The support of a permutation is the same as the support of its inverse.
Examplesopen allclose all
Basic Examples (2)
Inverse of a permutation:
Their product gives the identity permutation:
Some permutations, called involutions, are their own inverse:
Generalizations & Extensions (1)
On symbolic expressions other than permutations the result is given in terms of PermutationPower:
Properties & Relations (4)
InversePermutation is equivalent to PermutationPower with exponent -1:
Inverting a permutation is equivalent to reversing its cycles:
For a permutation of finite degree, its inverse can always be obtained as the power with a positive integer:
Ordering gives the inverse of a permutation list: