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Derangements

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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Derangements -

Tag(s) : Combinatorics,Mathematics

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Derangements

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Derangements Generator






Counting Derangements


Also on dCode: SubfactorialPermutations

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 permutationshref and remove those with fixed points (elements having an identical position in the permutationhref and in the starting position).

The set A,B,C has 6 permutationshref: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

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.

It remains 3 permutationshref C,A,B B,C,A et C,B,A that are the derangements.

How to count derangement?

Counting derangements uses subfactorials $$ !n = n! \sum_{k=0}^n \frac {(-1)^k}{k!} $$

For n items, the number of derangements is equal to !n (subfactorialhref 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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