具有特殊顶点的单纯排列
Simplicial arrangements with special vertex
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中文总结 AI 辅助
研究用任意有限超平面排列代替Weyl排列形成的具有特殊顶点的排列，核心方法未提及，主要贡献是证明某些此类单纯排列中直线平行类数量至多为12。
中文摘要 AI 辅助
Shi - Catalan和仿射Weyl排列以类似方式获得：它们由嵌入高维空间的Weyl排列以及平移副本组成。我们考虑更一般的情况，即用任意有限超平面排列代替Weyl排列。这样的排列称为具有特殊顶点的排列。作为主要结果，我们证明了某些具有特殊顶点的单纯排列中直线的平行类数量至多为12。
英文摘要
Shi-Catalan and affine Weyl arrangements are obtained in a similar way: they consist of a Weyl arrangement embedded into a higher dimensional space together with shifted copies. We consider the more general case when the Weyl arrangement is replaced by an arbitrary finite arrangement of hyperplanes. Such an arrangement is called an arrangement with special vertex. As our main result we prove that the number of parallel classes of lines in certain simplicial arrangements with special vertex is at most 12.
