Permutation Notations

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The number of ways to arrange seven objects in a row is . The arrangements are called permutations. Combinatorialists use two notational systems for permutations.


The first notation has positions on top and numbers of the rearranged objects on the bottom. It can be read as a mapping of a finite set of numbers, where the numbers on top get mapped to those below.

The second notation applies that mapping repeatedly to any starting number until there is a repetition. Then a new number is chosen to start the next cycle, and so on. A permutation can be shown as a directed graph.


Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA




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