Snapshot 1: There is only one way to permute a list containing
elements into
(singleton) cycles, and therefore
.
Snapshot 2: Rotating the elements in a cycle so that the last becomes the first results in the same cycle:
is the same cycle as
. Because of this, it is often desirable to choose a standard representation of any cycle, such as rotating it so that its greatest element is listed first. After fixing the position of the greatest element in a list of
items, there are
ways to permute the remaining
elements to create different cycles, which means that
.
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