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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 method of distinguished element ： ウィキペディア英語版 method of distinguished element In enumerative combinatorial mathematics, identities are sometimes established by arguments that rely on singling out one "distinguished element" of a set. ==Definition== Let $\backslash mathcal$ be a family of subsets of the set $A$ and let $x\; \backslash in\; A$ be a distinguished element of set $A$. Then suppose there is a predicate $P(X,x)$ that relates a subset $X\backslash subseteq\; A$ to $x$. Denote $\backslash mathcal(x)$ to be the set of subsets $X$ from $\backslash mathcal$ for which $P(X,x)$ is true and $\backslash mathcal-x$ to be the set of subsets $X$ from $\backslash mathcal$ for which $P(X,x)$ is false, Then $\backslash mathcal(x)$ and $\backslash mathcal-x$ are disjoint sets, so by the method of summation, the cardinalities are additive :$|\backslash mathcal|\; =\; |\backslash mathcal(x)|\; +\; |\backslash mathcal-x|$ Thus the distinguished element allows for a decomposition according to a predicate that is a simple form of a divide and conquer algorithm. In combinatorics, this allows for the construction of recurrence relations. Examples are in the next section. 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「method of distinguished element」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.