On Smith normal forms of \(q\)-Varchenko matrices
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...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2006 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
|---|