翻訳と辞書 Words near each other ・ Dual ignition ・ Dual impedance ・ Dual in-line package ・ Dual income tax ・ Dual Independent Map Encoding ・ Dual inheritance theory ・ Dual intent ・ Dual kingship ・ Dual labour market ・ Dual language ・ Dual loop ・ Dual loyalty ・ Dual loyalty (ethics) ・ Dual mandate ・ Dual mass flywheel ・ Dual matroid ・ Dual messiahs ・ Dual mode mobile ・ Dual mode propulsion rocket ・ Dual modular redundancy ・ Dual module ・ Dual monarchy ・ Dual monarchy of England and France ・ Dual Mono ・ Dual naming ・ Dual narrative ・ Dual norm ・ Dual number ・ Dual object ・ Dual of BCH is an independent source 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 Dual matroid ： ウィキペディア英語版 Dual matroid In matroid theory, the dual of a matroid $M$ is another matroid $M^\backslash ast$ that has the same elements as $M$, and in which a set is independent if and only if $M$ has a basis set disjoint from it.〔.〕〔.〕〔.〕 Matroid duals go back to the original paper by Hassler Whitney defining matroids.〔. Reprinted in , pp. 55–79. See in particular section 11, "Dual matroids", pp. 521–524.〕 They generalize to matroids the notions of planar graph duality and of dual spaces in linear algebra. ==Basic properties== Duality is an involution: for all $M$, $(M^\backslash ast)^\backslash ast=M$.〔〔〔 An alternative definition of the dual matroid is that its basis sets are the complements of the basis sets of $M$. The basis exchange axiom, used to define matroids from their bases, is self-complementary, so the dual of a matroid is necessarily a matroid.〔 The flats of $M$ are complementary to the cycles (unions of circuits) of $M^\backslash ast$, and vice versa.〔 If $r$ is the rank function of a matroid $M$ on ground set $E$, then the rank function of the dual matroid is $r^\backslash ast(S)=r(E\; \backslash setminus\; S)+|S|-r(E)$.〔〔〔 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「Dual 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.