On Smith normal forms of \(q\)-Varchenko matrices

• Date: 2023
• Main Authors: Boulware, N., Jing, N., Misra, K. C.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: Smith normal forms; hyperplane arrangements; Platonic solids; Varchenko matrices; 15A21; 05E18; 52C35
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2006
• Journal Title: Algebra and Discrete Mathematics

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...