A permutation with no fixed points. Any rotation is of this form, but the converse is not true for permutations on more than 3 elements.

The number of derangements of n elements is the integer closest to n!/e. This is the poster child for showing a use of the inclusion / exclusion principle (aka Poincare's method) -- see the node about counting fixed points of permutations.

To clarify ariels definition of derangement, with respect to combinatorics, it is a rearrangement of an ordered set of things so that no element is in its original position.

--back to combinatorics--

De*range"ment (?), n. [Cf. F. d'erangement.]

The act of deranging or putting out of order, or the state of being deranged; disarrangement; disorder; confusion; especially, mental disorder; insanity.

Syn. -- Disorder; confusion; embarrassment; irregularity; disturbance; insanity; lunacy; madness; delirium; mania. See Insanity.

 

© Webster 1913.

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