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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Monoid factorisation ： ウィキペディア英語版 Monoid factorisation In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let ''A'' * be the free monoid on an alphabet ''A''. Let ''X''''i'' be a sequence of subsets of ''A'' * indexed by a totally ordered index set ''I''. A factorisation of a word ''w'' in ''A'' * is an expression :$w\; =\; x\_\; x\_\; \backslash cdots\; x\_\; \backslash$ with $x\_\; \backslash in\; X\_$ and $i\_1\; \backslash ge\; i\_2\; \backslash ge\; \backslash ldots\; \backslash ge\; i\_n$. ==Chen–Fox–Lyndon theorem== A ''Lyndon word'' over a totally ordered alphabet ''A'' is a word which is lexicographically less than all its rotations.〔Lothaire (1997) p.64〕 The Chen–Fox–Lyndon theorem states that every string may be formed in a unique way by concatenating a non-increasing sequence of Lyndon words. Hence taking ''X''''l'' to be the singleton set for each Lyndon word ''l'', with the index set ''L'' of Lyndon words ordered lexicographically, we obtain a factorisation of ''A'' *.〔Lothaire (1997) p.67〕 Such a factorisation can be found in linear time.〔.〕 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「Monoid factorisation」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.