On the Smith normal form of Varchenko matrix - Cai, Tommy Wuxing (Ars mathematica contemporanea, 2020)
Let ?$\mathcal{A}$? be a hyperplane arrangement in ?$\mathbb{A}$? isomorphic to ?$\mathbb{R}^n$?. Let ?$\mathbb{R}^n$? be the ?$q$?-Varchenko matrix for the arrangement ?$\mathcal{A}$? 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 ?$\mathcal{Z}q$?.
Keywords: hyperplane arrangement; sestav hiperravnin; Smith normal form; Smithova normalna oblika; Varchenko matrix; Varchenkova matrika