A random permutation is a permutation containing a fixed number 
of a random selection from a given set of elements. There are two main algorithms
for constructing random permutations. The first constructs a vector of random real
numbers and uses them as keys to records containing the integers 1 to 
. The second starts with an arbitrary permutation and then
exchanges the 
th
element with a randomly selected one from the first 
elements for 
, ..., 
(Skiena 1990).
A random permutation on the integers 
can be implemented in the Wolfram
Language as RandomSample[Range[n]].
A random permutation in the permutation graph pg
can be computed using RandomPermutation[pg],
and 
such random permutations by RandomPermutation[pg,
n]. 
random permutations in the symmetric group of
order 
can be computed using RandomPermutation[d,
n].
There are an average of 
permutation inversions
in a permutation on 
elements (Skiena 1990, p. 29). The expected number of
permutation cycles of length 1 in a random permutation over the symmetric group 
is 1.
