定向拟阵的Varchenko矩阵的对角形式
Diagonal form of the Varchenko matrices for oriented matroids
摘要：
由Alexandre Varchenko首先引入的超平面排列的Varchenko矩阵的构造自然地扩展到定向拟阵。本文推广了Gao和Zhang的定理，证明了定向拟阵的Varchenko矩阵具有对角形式当且仅当对应于该定向拟阵的伪超平面排列处于半一般位置，即不包含退化.此外，我们证明了伪线排列的Varchenko矩阵具有块对角形式。这也为二维Varchenko矩阵行列式公式提供了另一种组合证明。
英文摘要：
The construction of the Varchenko matrix for hyperplane arrangements, first introduced by Alexandre Varchenko, extends naturally to oriented matroids. In this paper, we generalize the theorem of Gao and Zhang by proving that the Varchenko matrix of an oriented matroid has a diagonal form if and only if the pseudohyperplane arrangement corresponding to the oriented matroid is in semigeneral position, i.e. it does not contain a degeneracy. Furthermore, we show that the Varchenko matrix of a pseudoline arrangement has a block diagonal form. This also provides an alternative combinatorial proof for the Varchenko matrix determinant formula in dimension two.
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