论文标题
定向基质的Varchenko矩阵的对角线形式
Diagonal form of the Varchenko matrices for oriented matroids
论文作者
论文摘要
Alexandre Varchenko首先引入的Varchenko矩阵用于超平面布置的构建自然而然地扩展到定向的矩阵。在本文中，我们通过证明且仅当且仅当对应于方向的矩阵的伪基层布置时，我们就会概括Gao和Zhang的定理，以证明定向矩阵的Varchenko矩阵具有对角线形式。 此外，我们表明伪线的varchenko矩阵具有块对角线形式。这也为VARCHENKO矩阵确定性公式提供了二维的替代组合证明。
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.
