| 对称无限布尔方阵的本原指数集的刻划 |
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| 引用本文： | 李修清,王敏.对称无限布尔方阵的本原指数集的刻划[J].系统科学与数学,2008,28(12):1478-1485. |
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| 作者姓名： | 李修清 王敏 |
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| 作者单位： | 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 |
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| 基金项目： | 广西壮族自治区教育厅科研基金([2006]26号)资助课题
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| 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}.
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| 关 键 词： | 对称无限布尔方阵 本原指数 本原图 直径 |
| 收稿时间： | 2006-10-24 |
On the Primitive Exponent Set of Symmetric Infinite BooleanMatrics |
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| LI Xiuqing,WANG Min.On the Primitive Exponent Set of Symmetric Infinite BooleanMatrics[J].Journal of Systems Science and Mathematical Sciences,2008,28(12):1478-1485. |
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| Authors: | LI Xiuqing WANG Min |
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| Institution: | (1)Guilin College of Aerospace Technology,Guilin 541004;(2)Department of Mathematics, YantaiUniversity, Yantai 264005 |
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| 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 E_d={1,2,...,2d}. |
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| Keywords: | Symmetric infinite Boolean matrices primitive exponent primitive graph diameter |
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