permutation
permutation of a set S. A bijection of S onto itself. When S is finite, a permutation can be portrayed as a rearrangement of the elements of S. The number of permutations of a set of n elements is n!
A permutation of the elements of {1,2,3} can be written 1 2 3 2 1 3
indicating that 1 is mapped into 2, 2 into 1, and 3 into 3. Alternatively the above can be written, using a cycle notation, as (1 2); this implies that the element 3 is unaltered but that 1 is mapped into 2 and 2 into 1.
For collections of elements in which repeated occurrences of items may exist, a permutation can be described as a rearrangement of elements in which each element appears with the same frequency as before.
A permutation of the elements of {1,2,3} can be written 1 2 3 2 1 3
indicating that 1 is mapped into 2, 2 into 1, and 3 into 3. Alternatively the above can be written, using a cycle notation, as (1 2); this implies that the element 3 is unaltered but that 1 is mapped into 2 and 2 into 1.
For collections of elements in which repeated occurrences of items may exist, a permutation can be described as a rearrangement of elements in which each element appears with the same frequency as before.
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permutation