Permutation diagrams

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A permutation of a set is a rearrangement of all its elements. (There are many special classes of permutations, such as derangements, which are permutations that leave no element in its original position.) Here are some diagrams that represent the n! possible permutations of a set with n elements.

3 elements, 6 permutations:
123, 132, 213, 231, 312, 321

4 elements, 24 permutations:
1234, 1243, 1324, 1342, ..., 4312, 4321

5 elements, 120 permutations:
12345, 12354, 12435, 12453, ..., 54321

6 elements, 720 permutations:
123456, 123465, 123546, ..., 654321

Designed and rendered on a Sunday using Mathematica 3.0 for the Apple Macintosh.

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