Periodicity of hyperplane arrangements with integral coefficients modulo positive integers
Combinatorics
2008-04-16 v2
Abstract
We study central hyperplane arrangements with integral coefficients modulo positive integers . 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 are periodic except for a finite number of 's.
Keywords
Cite
@article{arxiv.math/0703904,
title = {Periodicity of hyperplane arrangements with integral coefficients modulo positive integers},
author = {Hidehiko Kamiya and Akimichi Takemura and Hiroaki Terao},
journal= {arXiv preprint arXiv:math/0703904},
year = {2008}
}