On Smith normal forms of $q$-Varchenko matrices
| Autor: | Boulware, Naomi, Jing, Naihuan, Misra, Kailash C. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Algebra and Discrete Math. 34:2 (2022), 187-222 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.12958/adm2006 |
| Popis: | 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. Comment: 22 pages, 8 figures |
| Databáze: | arXiv |
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