Orientability of matroids
Orientability of matroids
复制标题
拟阵的定向性
DOI：
10.1016/0095-8956(78)90080-1
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
M. Vergnas
中科院分区：
文献类型：
--
作者：
R. Bland;M. Vergnas
在本文中，我们定义定向拟阵和发展其基本性质，从而导致推广已知的结果，有向图，凸多面体和线性规划。定义了定向拟阵的对偶和子阵。它表明，每一个坐标化（表示）的有序域上的拟阵诱导定向的拟阵。的拟阵是定向的，但不coordinatizable和拟阵是不定向的例子。我们证明了一个二元拟阵是定向的当且仅当它是么模（正则），并且每个么模拟阵都有一个由坐标化诱导的方向，并且在某种简单的意义上是唯一的。
In this paper we define oriented matroids and develop their fundamental properties, which lead to generalizations of known results concerning directed graphs, convex polytopes, and linear programming. Duals and minors of oriented matroids are defined. It is shown that every coordinatization (representation) of a matroid over an ordered field induces an orientation of the matroid. Examples of matroids that are orientable but not coordinatizable and of matroids that are not orientable are presented. We show that a binary matroid is orientable if and only if it is unimodular (regular), and that every unimodular matroid has an orientation that is induced by a coordinatization and is unique in a certain straightforward sense.