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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 Paving matroid ： ウィキペディア英語版 Paving matroid In the mathematical theory of matroids, a paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid of rank $r$ every circuit has size at most $r+1$, so it is equivalent to define paving matroids as the matroids in which the size of every circuit belongs to the set $\backslash$.〔.〕 It has been conjectured that almost all matroids are paving matroids. ==Examples== Every simple matroid of rank three is a paving matroid; for instance this is true of the Fano matroid. The Vámos matroid provides another example, of rank four. Uniform matroids of rank $r$ have the property that every circuit is of length exactly $r+1$ and hence are all paving matroids; the converse does not hold, for example, the cycle matroid of the complete graph $K\_4$ is paving but not uniform. A Steiner system $S(t,k,v)$ is a pair $(S,\backslash mathcal)$ where $S$ is a finite set of size $v$ and $\backslash mathcal$ is a family of $k$-element subsets of $S$ with the property that every $t$-element subset of $S$ is also a subset of exactly one set in $\backslash mathcal$. The elements of $\backslash mathcal$ form a $t$-partition of $S$ and hence are the hyperplanes of a paving matroid on $S$. 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「Paving matroid」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.