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If is a permutation then the order of is the least natural
number such that
. The order of the permutation
is the lcm of the lengths of the cycles in the disjoint cycle decomposition
of .
In card shuffling we need to maximise the order of the relevant permutation
. One can show (see) that for of maximal length we can take
all the cycles in the disjoint cycle representation to have prime power length.
For instance with cards we can get a
with an order of
(cycle type
).

root
2002-06-10