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

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.