caa a22 4500 445855568 CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00026-011-0105-6 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0105-6 Periodicity of Non-Central Integral Arrangements Modulo Positive Integers [Elektronische Daten] [Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao] An integral coefficient matrix determines an integral arrangement of hyperplanes in $${\mathbb{R}^m}$$ . After modulo q reduction $${(q \in {\mathbb{Z}_{ >0 }})}$$ , the same matrix determines an arrangement $${\mathcal{A}_q}$$ of "hyperplanes” in $${\mathbb{Z}^m_q}$$ . In the special case of central arrangements, Kamiya, Takemura, and Terao [J. Algebraic Combin. 27(3), 317-330 (2008)] showed that the cardinality of the complement of $${\mathcal{A}_q}$$ in $${\mathbb{Z}^m_q}$$ is a quasi-polynomial in $${q \in {\mathbb{Z}_{ >0 }}}$$ . Moreover, they proved in the central case that the intersection lattice of $${\mathcal{A}_q}$$ is periodic from some q on. The present paper generalizes these results to the case of non-central arrangements. The paper also studies the arrangement $${\hat{\mathcal{B}}_m^{[0,a]}}$$ of Athanasiadis [J. Algebraic Combin. 10(3), 207-225 (1999)] to illustrate our results. Springer Basel AG, 2011 characteristic quasi-polynomial nationallicence elementary divisor nationallicence hyperplane arrangement nationallicence intersection poset nationallicence Kamiya Hidehiko Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, 464-8601, Nagoya, Japan aut Takemura Akimichi Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-0033, Tokyo, Japan aut Terao Hiroaki Department of Mathematics, Hokkaido University, North 10, West 8, Kita-ku, 060-0810, Sapporo, Japan aut Annals of Combinatorics SP Birkhäuser Verlag Basel 15/3(2011-09-01), 449-464 0218-0006 15:3<449 2011 15 26 https://doi.org/10.1007/s00026-011-0105-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0105-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kamiya Hidehiko Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, 464-8601, Nagoya, Japan aut NATIONALLICENCE 700 1- Takemura Akimichi Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-0033, Tokyo, Japan aut NATIONALLICENCE 700 1- Terao Hiroaki Department of Mathematics, Hokkaido University, North 10, West 8, Kita-ku, 060-0810, Sapporo, Japan aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/3(2011-09-01), 449-464 0218-0006 15:3<449 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer