JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (2): 51-57.doi: 10.6040/j.issn.1671-9352.0.2013.416

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The algorithms of characteristic polynomial and supersolvability#br#  of a hyperplane arrangement

GAO Rui-mei1, PEI Dong-he2   

  1. 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
  • Received:2013-09-04 Online:2014-02-20 Published:2014-06-04

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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 characteristic matrix can be changed into calculating the rank of the sub-matrices of the coefficient matrix. The algorithm of characteristic 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.

Key words: hyperplane arrangement, supersolvability, characteristic polynomial

CLC Number: 

  • O189
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