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Cycles from Permutations

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permutation length
10
new random permutation of the same length
permutation
{4,8,3,7,6,10,2,5,1,9}
cycles
(4, 7, 2, 8, 5, 6, 10, 9, 1) (3)
A permutation is a list in which each element occurs only once. If the members of the permutation have values
1,…,n
, where
n
is the length of the permutation, then you can think of a permutation as an "onto" ("surjective") function of the set
{1,2,…,n}
to itself. If you successively apply this function to any member of the set, you obtain its "cycle" or "orbit". This Demonstration shows how you can write a permutation as a list of these cycles and how these cycles can be visualized as a graph.
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