On the Smith normal form of the Varchenko matrix

作者：Cai, Tommy Wuxing; Chen, Yue; Mu, Lili^*

来源：ARS Mathematica Contemporanea, 2020, 19(2): 351-362.

DOI：10.26493/1855-3974.2262.9b8

• Hyperplane arrangement
• Smith normal form
• Varchenko matrix

Let A be a hyperplane arrangement in A isomorphic to R-n. Let V-q be the q-Varchenko matrix for the arrangement A with all hyperplane parameters equal to q. In this paper, we consider three interesting cases of q-Varchenko matrices associated to hyperplane arrangements. We show that they have a Smith normal form over Z[q].