A catalogue of simplicial arrangements in the real projective plane
A catalogue of simplicial arrangements in the real projective plane
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真实射影平面上的单纯排列目录
DOI：
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发表时间：
2009
期刊：
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通讯作者：
B. Grünbaum
中科院分区：
文献类型：
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作者：
B. Grünbaum
排列是在实射影平面上由不构成铅笔的有限直线族生成的复数。排列的面是直线并集的补集的连通分量。如果一个排列的所有面都是单纯的(三角形)，则该排列是单纯的。本文件更新了近40年前出版的唯一一份简单安排目录，并以非常简明的形式提出。单纯的安排常常为各种问题提供最优解。一个似乎非常困难的问题是，判断这里展示的集合是否是简单安排的完整列表。
An arrangement is the complex generated in the real projective plane by a finite family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the union of lines. An arrangement is simplicial if all its faces are simplices (triangles). The present paper updates the only previous catalogue of simplicial arrangements, published almost 40 years ago, and presented in a very condensed form. The simplicial arrangements often provide optimal solutions for various problems. A problem that seems very hard is to decide whether the collection presented here is a complete listing of simplicial arrangements.