Geodesic
Periodicity of hyperplane arrangements with integral coefficients modulo positive integers
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 3, pp. 317-330.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords characteristic polynomial, Ehrhart quasi-polynomial, elementary divisor, hyperplane arrangement, intersection lattice 
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     author = {Kamiya, Hidehiko and Takemura, Akimichi and Terao, Hiroaki},
     title = {Periodicity of hyperplane arrangements with integral coefficients modulo positive integers},
     journal = {Journal of Algebraic Combinatorics},
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Kamiya, Hidehiko; Takemura, Akimichi; Terao, Hiroaki. Periodicity of hyperplane arrangements with integral coefficients modulo positive integers. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 3, pp. 317-330. http://geodesic.mathdoc.fr/item/JAC_2008__27_3_a3/