翻訳と辞書 Words near each other ・ Symmetric convolution ・ Symmetric decreasing rearrangement ・ Symmetric derivative ・ Symmetric difference ・ Symmetric digital subscriber line ・ Symmetric equilibrium ・ Symmetric federalism ・ Symmetric function ・ Symmetric game ・ Symmetric graph ・ Symmetric group ・ Symmetric Hash Join ・ Symmetric hydrogen bond ・ Symmetric hypergraph theorem ・ Symmetric in Design ・ Symmetric inverse semigroup ・ Symmetric level-index arithmetic ・ Symmetric matrix ・ Symmetric mean absolute percentage error ・ Symmetric monoidal category ・ Symmetric multiprocessing ・ Symmetric multiprocessor system ・ Symmetric obstruction theory ・ Symmetric Phase Recording ・ Symmetric polynomial ・ Symmetric probability distribution ・ Symmetric product ・ Symmetric product of an algebraic curve ・ Symmetric rank-one ・ Symmetric relation Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Symmetric inverse semigroup ： ウィキペディア英語版 Symmetric inverse semigroup __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 $\backslash mathcal\_X$〔Hollings 2014, p. 252〕 or $\backslash mathcal\_X$〔Ganyushkin and Mazorchuk 2008, p. v〕 In general $\backslash mathcal\_X$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.