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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.

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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.

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

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