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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 interval order ： ウィキペディア英語版 interval order In mathematics, especially order theory, the interval order for a collection of intervals on the real line is the partial order corresponding to their left-to-right precedence relation—one interval, ''I''1, being considered less than another, ''I''2, if ''I''1 is completely to the left of ''I''2. More formally, a poset $P\; =\; (X,\; \backslash leq)$ is an interval order if and only if there exists a bijection from $X$ to a set of real intervals, so $x\_i\; \backslash mapsto\; (\backslash ell\_i,\; r\_i)$, such that for any $x\_i,\; x\_j\; \backslash in\; X$ we have in $P$ exactly when . Such posets may be equivalently characterized as those with no induced subposet isomorphic to the pair of two element chains, the $(2+2)$ free posets . The subclass of interval orders obtained by restricting the intervals to those of unit length, so they all have the form $(\backslash ell\_i,\; \backslash ell\_i\; +\; 1)$, is precisely the semiorders. The complement of the comparability graph of an interval order ($X$, ≤) is the interval graph $(X,\; \backslash cap)$. Interval orders should not be confused with the interval-containment orders, which are the containment orders on intervals on the real line (equivalently, the orders of dimension ≤ 2). == Interval dimension == The interval dimension of a partial order can be defined as the minimal number of interval order extensions realizing this order, in a similar way to the definition of the order dimension which uses linear extensions. The interval dimension of an order is always less than its order dimension,〔http://page.math.tu-berlin.de/~felsner/Paper/Idim-dim.pdf p.2〕 but interval orders with high dimensions are known to exist. While the problem of determining the order dimension of general partial orders is known to be NP-complete, the complexity of determining the order dimension of an interval order is unknown.〔http://page.math.tu-berlin.de/~felsner/Paper/diss.pdf, p.47〕 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「interval order」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.