InversePermutation¶

Returns the inverse of a permutation given in list form.

$ wo 'InversePermutation[{2, 3, 1}]'
{3, 1, 2}

Also accepts a permutation in disjoint cycle form. Each cycle is reversed and rotated so its smallest element comes first; cycles are then sorted by their smallest element.

$ wo 'InversePermutation[Cycles[{{3, 2, 5, 1}, {4, 7}}]]'
Cycles[{{1, 5, 2, 3}, {4, 7}}]

Involutions are their own inverse:

$ wo 'InversePermutation[Cycles[{{1, 2}, {3, 4}}]]'
Cycles[{{1, 2}, {3, 4}}]