论文标题
关于史密斯的正常形式$ q $ -Varchenko矩阵
On Smith normal forms of $q$-Varchenko matrices
论文作者
论文摘要
在本文中，我们调查了$ q $ -Varchenko矩阵，以在两个和三个维度的对称性上进行某些超平面布置，并证明它们在$ \ Mathbb z [q] $上具有史密斯正常形式。特别是，我们检查了平面中常规$ n $ gon的超平面布置以及空间和柏拉图式Polyhedra中的二面模型。在每种情况下，我们都证明与超平面布置相关的$ q $ -Varchenko矩阵具有超过$ \ mathbb z [q] $的史密斯正常形式，并意识到他们在$ \ mathbb z [q] $上的一致转换矩阵。
In this paper, we investigate $q$-Varchenko matrices for some hyperplane arrangements with symmetry in two and three dimensions, and prove that they have a Smith normal form over $\mathbb Z[q]$. In particular, we examine the hyperplane arrangement for the regular $n$-gon in the plane and the dihedral model in the space and Platonic polyhedra. In each case, we prove that the $q$-Varchenko matrix associated with the hyperplane arrangement has a Smith normal form over $\mathbb Z[q]$ and realize their congruent transformation matrices over $\mathbb Z[q]$ as well.
