Inverse Permutation

An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example,


are inverse permutations, since the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in p_1 are p_2, and the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in p_2 are likewise p_1 (Muir 1960, p. 5).

The inverse permutation of a given permutation p can be computed in the Wolfram Language using InversePermutation[p].

Inverse permutations are sometimes also called conjugate or reciprocal permutations (Muir 1960, p. 4).

See also

Permutation, Permutation Inversion, Self-Conjugate Partition

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Muir, T. A Treatise on the Theory of Determinants. New York: Dover, 1960.

Referenced on Wolfram|Alpha

Inverse Permutation

Cite this as:

Weisstein, Eric W. "Inverse Permutation." From MathWorld--A Wolfram Web Resource.

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