Periodicity of non-central integral arrangements modulo positive integers
Periodicity of non-central integral arrangements modulo positive integers
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以正整数为模的非中心积分排列的周期性
DOI：
10.1007/s00026-011-0105-6
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发表时间：
2011
影响因子：
0.5
通讯作者：
A. Takemura and Hiroaki Terao
中科院分区：
文献类型：
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作者：
Hidehiko Kamiya;A. Takemura and Hiroaki Terao
中的超平面的积分排列由一个积分系数矩阵决定。经过模约简后，同一矩阵确定了中“超平面”的排列。在中心布置的特殊情况下，Kamiya， Takemura和Terao [J]。代数组合，27(3),317-330(2008)]证明了补的基数是中的拟多项式。此外，在中心情况下，他们证明了交点格是周期性的。本文将这些结果推广到非中心布置的情况。本文还研究了亚thanasiadis的排列[J]。代数组合，10(3),207-225(1999)]来说明我们的结果。
An integral coefficient matrix determines an integral arrangement of hyperplanes in. After moduloqreduction, the same matrix determines an arrangementof “hyperplanes” in. 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 ofinis a quasi-polynomial in. Moreover, they proved in the central case that the intersection lattice ofis periodic from someqon. The present paper generalizes these results to the case of non-central arrangements. The paper also studies the arrangementof Athanasiadis [J. Algebraic Combin. 10(3), 207–225 (1999)] to illustrate our results.