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What is a permutation?

What is a permutation? Here are some definitions.

Noun
  1. One of the ways something exists, or the ways a set of objects can be ordered.
  2. (mathematics) A one-to-one mapping from a finite set to itself.
  3. (mathematics) An ordering of a finite set of distinct elements.
  4. (music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.
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Examples
Another permutation could be to cut spending and taxes and retire the national debt.
One of the areas which his work took him into was infinite permutation groups.
Netto made major steps towards abstract group theory when he combined permutation group results and groups in number theory.
Significance thresholds for each trait were determined by permutation and are denoted by dashed lines with the same color code as the traits.
Chromosome-wide significance thresholds were determined by permutation as previously described.
Binah defines what is possible from the unlimited permutation of infinite creativity.

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