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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 Partial geometry ： ウィキペディア英語版 Partial geometry An incidence structure $C=(P,L,I)$ consists of points $P$, lines $L$, and flags $I\; \backslash subseteq\; P\; \backslash times\; L$ where a point $p$ is said to be incident with a line $l$ if $(p,l)\; \backslash in\; I$. It is a (finite) partial geometry if there are integers $s,t,\backslash alpha\backslash geq\; 1$ such that: * For any pair of distinct points $p$ and $q$, there is at most one line incident with both of them. * Each line is incident with $s+1$ points. * Each point is incident with $t+1$ lines. * If a point $p$ and a line $l$ are not incident, there are exactly $\backslash alpha$ pairs $(q,m)\backslash in\; I$, such that $p$ is incident with $m$ and $q$ is incident with $l$. A partial geometry with these parameters is denoted by $pg(s,t,\backslash alpha)$. ==Properties== * The number of points is given by $\backslash frac$ and the number of lines by $\backslash frac$. * The point graph of a $pg(s,t,\backslash alpha)$ is a strongly regular graph : $srg((s+1)\backslash frac,s(t+1),s-1+t(\backslash alpha-1),\backslash alpha(t+1))$. * Partial geometries are dual structures : the dual of a $pg(s,t,\backslash alpha)$ is simply a $pg(t,s,\backslash alpha)$. 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「Partial geometry」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.