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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 Lyndon word ： ウィキペディア英語版 Lyndon word In mathematics, in the areas of combinatorics and computer science, a Lyndon word is a string that is strictly smaller in lexicographic order than all of its rotations. Lyndon words are named after mathematician Roger Lyndon, who introduced them in 1954, calling them standard lexicographic sequences.〔; ; .〕 ==Definitions== Several equivalent definitions are possible. A ''k''-ary Lyndon word of length ''n'' is an ''n''-character string over an alphabet of size ''k'', and which is the minimum element in the lexicographical ordering of all its rotations. Being the singularly smallest rotation implies that a Lyndon word differs from any of its non-trivial rotations, and is therefore aperiodic.〔; .〕 Alternately, a Lyndon word has the property that, whenever it is split into two substrings, the left substring is always lexicographically less than the right substring. That is, if ''w'' is a Lyndon word, and ''w'' = ''uv'' is any factorization into two substrings, with ''u'' and ''v'' understood to be non-empty, then ''u'' < ''v''. This definition implies that ''w'' is a Lyndon word if and only if there exist Lyndon words ''u'' and ''v'' such that ''u'' < ''v'' and ''w'' = ''uv''.〔 Although there may be more than one choice of ''u'' and ''v'' with this property, there is a particular choice, called the ''standard factorization'', in which ''v'' is as long as possible.〔.〕 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「Lyndon word」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.