Function Repository Resource:

DerangementQ

Test whether a permutation is a derangement

Contributed by: Wolfram Staff

ResourceFunction["DerangementQ"][p]

tests whether the permutation p is such that no element appears in its original position.

Details

The permutation can be given in either permutation list or disjoint cyclic format.

No elements are in their original places:

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For even n, the list {n,…,3,2,1} is a derangement:

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Test if a permutation in disjoint cycle format is a derangement:

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The chances are about 1 in 3 that a permutation is a derangement:

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