翻訳と辞書 Words near each other ・ Interxion ・ Interval (play) ・ Interval arithmetic ・ Interval boundary element method ・ Interval chromatic number of an ordered graph ・ Interval class ・ Interval contractor ・ Interval cycle ・ Interval edge coloring ・ Interval estimation ・ Interval exchange transformation ・ Interval finite element ・ Interval graph ・ Interval International ・ Interval Monday ・ Interval order ・ Interval propagation ・ Interval ratio ・ Interval recognition ・ Interval Research Corporation ・ Interval scheduling ・ Interval signal ・ Interval temporal logic ・ Interval training ・ Interval tree ・ Interval vector ・ Intervale ・ Intervale (Augusta County, Virginia) ・ Intervale Avenue (IRT White Plains Road Line) ・ Intervale Factory Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

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.