An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example,
 |  |  |
(1)
|
 |  |  |
(2)
|
are inverse permutations, since the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in 
are 
,
and the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in 
are likewise 
(Muir 1960, p. 5).
The inverse permutation of a given permutation 
can be computed in the Wolfram
Language using InversePermutation[p].
Inverse permutations are sometimes also called conjugate or reciprocal permutations (Muir 1960, p. 4).
