| 构形的特征多项式和超可解性的算法 |
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| 引用本文： | 高瑞梅,裴东河.构形的特征多项式和超可解性的算法[J].山东大学学报(自然科学版),2014(2):51-57. |
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| 作者姓名： | 高瑞梅 裴东河 |
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| 作者单位： | [1]长春理工大学理学院,吉林长春130022 [2]东北师范大学数学与统计学院,吉林长春130024 |
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| 基金项目： | 国家自然科学基金资助项目（11271063,11326078）;黑龙江省教育厅科技研究项目（12531187） |
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| 摘 要： | 给出了中心构形的系数矩阵、特征矩阵的定义，证明了中心构形的秩等于其系数矩阵的秩，将求构形的特征矩阵问题转化为系数矩阵的子矩阵求秩问题，给出中心构形的特征多项式的算法。研究了模元的一些性质，给出判断模元的一个等价条件，利用此条件简化判断模元的过程，给出判断中心构形超可解性的算法。
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| 关 键 词： | 超平面构形 特征多项式 超可解性 |
The algorithms of characteristic polynomial and supersolvability of a hyperplane arrangement |
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| GAO Rui-mei,PEI Dong-he.The algorithms of characteristic polynomial and supersolvability of a hyperplane arrangement[J].Journal of Shandong University(Natural Science Edition),2014(2):51-57. |
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| Authors: | GAO Rui-mei PEI Dong-he |
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| Institution: | 1. Department of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China; 2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, China) |
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| Abstract: | The definitions of coefficient matrix and characteristic matrix for a central arrangement are given.We obtain the conclusion that the rank of a central arrangement equals to the rank of its coefficient matrix.Calculating characteris-tic matrix can be changed into calculating the rank of the sub-matrices of the coefficient matrix.The algorithm of char-acteristic polynomial of a central arrangement is provided.We study some properties of a modular element, and give a equivalent condition of judging a modular element, which simplifies the procedure of looking for a modular element. Based on this result, the algorithm of supersolvability of a central arrangement is offered. |
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| Keywords: | hyperplane arrangement characteristic polynomial supersolvability |
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