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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 Word metric ： ウィキペディア英語版 Word metric In group theory, a branch of mathematics, a word metric on a group $G$ is a way to measure distance between any two elements of $G$. As the name suggests, the word metric is a metric on $G$, assigning to any two elements $g$, $h$ of $G$ a distance $d(g,h)$ that measures how efficiently their difference $g^\; h$ can be expressed as a word whose letters come from a generating set for the group. The word metric on G is very closely related to the Cayley graph of G: the word metric measures the length of the shortest path in the Cayley graph between two elements of G. A generating set for $G$ must first be chosen before a word metric on $G$ is specified. Different choices of a generating set will typically yield different word metrics. While this seems at first to be a weakness in the concept of the word metric, it can be exploited to prove theorems about geometric properties of groups, as is done in geometric group theory. == Examples == 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「Word metric」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.