Tool for generating derangements. In mathematics, a derangement is a permutation of distinct objects without fixed point, ie that no object is in its original position.

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Tool for generating derangements. In mathematics, a derangement is a permutation of distinct objects without fixed point, ie that no object is in its original position.

Answers to Questions

How to generate derangement?

To generate the list of derangements of a set, you have to list the permutations and remove those with fixed points (elements having an identical position in the permutation and in the starting position).

Example: The set A,B,C has 6 permutations: A,B,CB,A,CC,A,BA,C,BB,C,AC,B,A

Example: You have to remove the one with fixed points, ie. with A in position 1, those with B in position 2 and those with C in position 3.

Example: It remains 3 permutationsC,A,BB,C,A et C,B,A that are the derangements.

Example: For n items, the number of derangements is equal to !n (subfactorial of n)

How to remove the limit when computing derangements?

Derangements makes exponential values. The more calculations there are, the more expensive are computer servers, so the large generations must be paid.

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