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In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set ''S'' is a bijection between two specified subsets of ''S''. That is, it is defined by two subsets ''U'' and ''V'' of equal size, and a one-to-one mapping from ''U'' to ''V''. Equivalently, it is a partial function on ''S'' that can be extended to a permutation.〔.〕〔.〕 ==Representation== It is common to consider the case when the set ''S'' is simply the set 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 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 :◊◊, ◊1, ◊2, 1◊, 2◊, 12, 21. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Partial permutation」の詳細全文を読む スポンサード リンク
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