On the Generation of Oriented Matroids
On the Generation of Oriented Matroids
复制标题
关于有向拟阵的生成
DOI：
10.1007/s004540010027
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发表时间：
2000
影响因子：
0.8
通讯作者：
António Guedes de Oliveira
中科院分区：
文献类型：
--
作者：
J. Bokowski;António Guedes de Oliveira
我们提供了一个多用途的算法生成有向拟阵。应用证明了Grünbaum的一个猜想，即每个闭的可定向2-流形都可以几何嵌入到R3中，即，没有自相交的平面三角形。我们可以特别证明，对于每个亏格g\geq 6，存在无限类可定向的三角化闭2-流形，它们不能被几何嵌入到欧氏3-空间中。我们的算法是有趣的，在其本身的权利作为一种工具，许多调查中，面向拟阵发挥了关键作用。
We provide a multiple purpose algorithm for generating oriented matroids. An application disproves a conjecture of Grünbaum that every closed triangulated orientable 2-manifold can be embedded geometrically inR3, i.e., with flat triangles and without self-intersections. We can show in particular that there exists an infinite class of orientable triangulated closed 2-manifolds for each genusg \geq 6that cannot be embedded geometrically in Euclidean 3-space. Our algorithm is interesting in its own right as a tool for many investigations in which oriented matroids play a key role.