Periodicity of hyperplane arrangements with integral coefficients modulo positive integers |
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Authors: | Hidehiko Kamiya Akimichi Takemura Hiroaki Terao |
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Institution: | (1) Faculty of Economics, Okayama University, Okayama, Japan;(2) Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan;(3) Department of Mathematics, Hokkaido University, Hokkaido, Japan |
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Abstract: | We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways, first via the theory
of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the
characteristic polynomial of the corresponding real arrangement. With the former approach, we also prove that intersection
lattices modulo q are periodic except for a finite number of q’s.
This work was supported by the MEXT and the JSPS. |
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Keywords: | Characteristic polynomial Ehrhart quasi-polynomial Elementary divisor Hyperplane arrangement Intersection lattice |
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