Partial permutation
Representation

It is common to consider the case when the set S is simply the set {1, 2,..., n } of the first n integers. In this case, a partial permutation may be represented by a string of n symbols, some of which are distinct numbers in the range from 1 to n {\displaystyle n} and the remaining ones of which are a special "hole" symbol ◊. In this formulation, the domain U of the partial permutation consists of the positions in the string that do not contain a hole, and each such position is mapped to the number in that position. For instance, the string "1 ◊ 2" would represent the partial permutation that maps 1 to itself and maps 3 to 2. The seven partial permutations on two items are
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