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.
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This work was supported by the MEXT and the JSPS.
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Kamiya, H., Takemura, A. & Terao, H. Periodicity of hyperplane arrangements with integral coefficients modulo positive integers. J Algebr Comb 27, 317–330 (2008). https://doi.org/10.1007/s10801-007-0091-2
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DOI: https://doi.org/10.1007/s10801-007-0091-2