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...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2023
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2006 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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