对称无限布尔方阵的本原指数集的刻划  

ON THE PRIMITIVE EXPONENT SET OF SYMMETRIC INFINITE BOOLEAN MATRICS

作　　者：李修清[1] 王敏[2] 

机构地区：[1]桂林航天工业高等专科学校计算机系,桂林541004 [2]烟台大学数学与信息科学系,烟台264005

出　　处：《系统科学与数学》2008年第12期1478-1485,共8页Journal of Systems Science and Mathematical Sciences

基　　金：广西壮族自治区教育厅科研基金([2006]26号)资助课题.

摘　　要：研究了对称无限布尔方阵,给出了对称无限布尔方阵为本原阵的一个充分必要条件,证明了具有有限直径d的对称无限布尔方阵的本原指数的上确界为2d,最后证明了直径不超过d的全体对称本原无限布尔方阵的本原指数集是E_d={1,2,…,2d}.Abstract Symmetric infinite Boolean matrices are considered. Firstly a sufficient and necessary condition is given for symmetric infinite Boolean matrices to become primitive matri- ces. Then it is shown that the lease upper bound of the primitive exponent set of the symmetric infinite Boolean matrices with diameter d is 2d. Finally it is proven that the primitive exponent set of symmetric infinite Boolean matrices with diameter no more than d is Ed {1, 2,…,2d）.

关 键 词：对称无限布尔方阵 本原指数 本原图 直径 

分 类 号：O157.5[理学—数学]