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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 Critical pair (order theory) ： ウィキペディア英語版 Critical pair (order theory) In order theory, a discipline within mathematics, a critical pair is a pair of elements in a partially ordered set that are incomparable but that could be made comparable without requiring any other changes to the partial order. Formally, let be a partially ordered set. Then a critical pair is an ordered pair of elements of with the following three properties: * and are incomparable in , *for every in , if then , and *for every in , if then . If is a critical pair, then the binary relation obtained from by adding the single relationship is also a partial order. The properties required of critical pairs ensure that, when the relationship is added, the addition does not cause any violations of the transitive property. A set of linear extensions of is said to ''reverse'' a critical pair in if there exists a linear extension in for which occurs earlier than . This property may be used to characterize realizers of finite partial orders: A nonempty set of linear extensions is a realizer if and only if it reverses every critical pair. ==References== *. 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「Critical pair (order theory)」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.