构形的特征多项式和超可解性的算法  

The algorithms of characteristic polynomial and supersolvability of a hyperplane arrangement

作　　者：高瑞梅[1] 裴东河[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2014年第2期51-57,共7页Journal of Shandong University(Natural Science)

基　　金：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)

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。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.

关 键 词：超平面构形 特征多项式 超可解性 

分 类 号：O189[理学—数学]