On the Smith normal form of Varchenko matrix

Tommy Wuxing Cai, Yue Chen, Lili Mu

Abstract


Let A be a hyperplane arrangement in A isomorphic to ℝn. Let Vq be the q-Varchenko matrix for the arrangement 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 ℤ[q].


Keywords


Hyperplane arrangement, Smith normal form, Varchenko matrix

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DOI: https://doi.org/10.26493/1855-3974.2262.9b8

ISSN: 1855-3974

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