2023-03-26T07:02:45Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696482022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Periodicity of hyperplane arrangements with integral coefficients modulo positive integersKamiya, HidehikoTakemura, AkimichiTerao, Hiroakiopen accesscharacteristic polynomialEhrhart quasi-polynomialelementary divisorhyperplane arrangementintersection lattice410We 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.Department of Mathematics, Hokkaido University2007-03-30engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83989http://hdl.handle.net/2115/6964810.14943/83989Hokkaido University Preprint Series in Mathematics839114https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69648/1/pre839.pdfapplication/pdf211.16 KB2007-03-30