Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

Details Periodicity of hyperplane arrangements with integral coefficients modulo positive integers Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

2007-03-30

arxiv.org/abs/math/0703904v2

J. Alg. Combin. 27 (2008), 317-330

Mathematics

Combinatorics

Scientific paper

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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