Higher bruhat orders and cyclic hyperplane arrangements
Higher bruhat orders and cyclic hyperplane arrangements
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更高的布鲁哈特阶和循环超平面排列
DOI：
10.1016/0040-9383(93)90019-r
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
G. Ziegler
中科院分区：
文献类型：
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作者：
G. Ziegler
我们研究了Manin & Schechtman [MaS]的高Bruhat阶，并-用反演集刻画它们，-用交替定向拟阵的一致扩张的偏序集（即，用一个新的定向伪平面对循环超平面的扩张）来识别它们，-表明这是一个格，但不是一般的格，-表明这是通过包含反演集来排序的。然而，它并不是按包含顺序排列的。这意味着包含反演集定义的偏序不同于一般的偏序。我们证明了的适当部分是同伦等价于。因此，-for和for。与此相反，我们发现仿射超平面排列的一致扩张偏序集一般不是分次的，甚至不是格，并且其固有部分并不总是同伦等价于。
We study the higher Bruhat ordersof Manin & Schechtman [MaS] and - characterize them in terms of inversion sets, - identify them with the posetsof uniform extensions of the alternating oriented matroidsfor(that is, with the extensions of a cyclic hyperplane arrangement by a new oriented pseudoplane), - show thatis a lattice forand for, but not in general, - show thatis ordered by inclusion of inversion sets forand for. However,is not ordered by inclusion. This implies that the partial orderdefined by inclusion of inversion sets differs fromin general. We show that the proper part ofis homotopy equivalent to. Consequently, -forand for. In contrast to this, we find that the uniform extension poset of an affine hyperplane arrangement is in general not graded and not a lattice even for, and that the proper part is not always homotopy equivalent to.