| GCD矩阵的一种推广 |
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| 引用本文： | 韩海清,刘花璐.GCD矩阵的一种推广[J].数学杂志,2012,32(3):529-534. |
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| 作者姓名： | 韩海清 刘花璐 |
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| 作者单位： | 湖北理工学院数理学院,湖北黄石,435003 |
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| 摘 要： | 本文研究了有限个正整数直积上的GCD矩阵.利用Mbius反演得到了直积上的GCD矩阵性质和GCD矩阵行列式的计算方法.进一步,把正整数直积上的GCD矩阵推广到一般偏序集直积上,得到了广义GCD矩阵的性质.
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| 关 键 词： | GCD矩阵 交半格 交矩阵 广义Euler函数 Mbius反演 |
A GENERALIZATION OF GCD MATRICES |
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| HAN Hai-qing
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LIU Hua-lu.A GENERALIZATION OF GCD MATRICES[J].Journal of Mathematics,2012,32(3):529-534. |
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| Authors: | HAN Hai-qing LIU Hua-lu |
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| Institution: | (School of Math.and Physics,Hubei Polytechnic University,Huangshi 435003,China) |
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| Abstract: | In this paper,we study GCD matrices on the direct product of some finite positive integer sets,and obtain the properties and the determinant calculation method of GCD matrices on the direct product by the Mbius inversion.Moreover,we generalize the GCD matrices to the direct product of general partially ordered sets and gain some properties of generalized GCD matrices. |
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| Keywords: | GCD matrix meet semi-lattice meet matrix generalized Euler function Mbius inversion |
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