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__NOTOC__ In abstract algebra, the set of all partial bijections on a set ''X'' (aka one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on ''X''. The conventional notation for the symmetric inverse semigroup on a set ''X'' is 〔Hollings 2014, p. 252〕 or 〔Ganyushkin and Mazorchuk 2008, p. v〕 In general is not commutative. Details about the origin of the symmetric inverse semigroup are available in the discussion on the origins of the inverse semigroup. ==Finite symmetric inverse semigroups== When ''X'' is a finite set , the inverse semigroup of one-one partial transformations is denoted by ''C''''n'' and its elements are called charts or partial symmetries.〔Lipscomb 1997, p. 1〕 The notion of chart generalizes the notion of permutation. A (famous) example of (sets of) charts are the hypomorphic mapping sets from the reconstruction conjecture in graph theory.〔Lipscomb 1997, p. xiii〕 The cycle notation of classical, group-based permutations generalizes to symmetric inverse semigroups by the addition of a notion called a ''path'', which (unlike a cycle) ends when it reaches the "undefined" element; the notation thus extended is called ''path notation''.〔Lipscomb 1997, p. xiii〕 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「symmetric inverse semigroup」の詳細全文を読む スポンサード リンク
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