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).