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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 partition matroid ： ウィキペディア英語版 partition matroid In mathematics, a partition matroid or partitional matroid is a matroid formed from a direct sum of uniform matroids.〔.〕 ==Definition== Let $B\_i$ be a collection of disjoint sets, and let $d\_i$ be integers with $0\backslash le\; d\_i\backslash le\; |B\_i|$. Define a set $I$ to be "independent" when, for every index $i$, $|I\backslash cap\; B\_i|\backslash le\; d\_i$. Then the sets that are independent sets in this way form the independent sets of a matroid, called a partition matroid. The sets $B\_i$ are called the blocks of the partition matroid. A basis of the matroid is a set whose intersection with every block $B\_i$ has size exactly $d\_i$, and a circuit of the matroid is a subset of a single block $B\_i$ with size exactly $d\_i+1$. The rank of the matroid is $\backslash sum\; d\_i$.〔.〕 Every uniform matroid $U\{\}^r\_n$ is a partition matroid, with a single block $B\_1$ of $n$ elements and with $d\_1=r$. Every partition matroid is the direct sum of a collection of uniform matroids, one for each of its blocks. In some publications, the notion of a partition matroid is defined more restrictively, with every $d\_i=1$. The partitions that obey this more restrictive definition are the transversal matroids of the family of disjoint sets given by their blocks.〔E.g., see . uses the broader definition but notes that the $d\_i=1$ restriction is useful in many applications.〕 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「partition 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.