Definition
Let be a finite set, and
be distinct elements of . The expression
denotes the cycle σ whose action is
For each index i,
where is taken to mean .
There are different expressions for the same cycle; the following all represent the same cycle:
A 1-element cycle such as (3) is the identity permutation. The identity permutation can also be written as an empty cycle, "".
Read more about this topic: Cycle Notation
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“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
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Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
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—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)