Tests for a permutation being a derangement
A derangement is a permutation which leaves no element fixed.
is.derangement(x)
| x | Object to be tested | 
A vector of Booleans corresponding to whether the permutations are derangements or not.
The identity permutation is problematic because it potentially has zero size.
The identity element is not a derangement, although the (zero-size) identity
cycle and permutation both return TRUE under the natural R idiom
all(P != seq_len(size(P))). 
Robin K. S. Hankin
id
is.derangement(rperm(16,4))
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