| The Characteristic Polynomial of the Mixed Arrangement |
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| 作者姓名： | SU Dan ZHANG Dunmu |
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| 作者单位： | [1]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China [2]School of Information Technology and Management Engineering, University of International Business and Economics,Beijing 100029, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China（10471020） |
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| 摘 要： | We consider the mixed arrangement which is com posed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mbius function of the mixed arrangement and the original hyperplane arangement. The Mbius function of the mixed arrangement is equal to the positive or the negative Mbius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement.
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| 关 键 词： | 特征多项式 混合排列 超平面 默比乌斯函数 |
| 文章编号： | 1007-1202（2007）02-0203-04 |
| 收稿时间： | 2006-03-07 |
The characteristic polynomial of the mixed arrangement |
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| SU Dan ZHANG Dunmu.The Characteristic Polynomial of the Mixed Arrangement[J].Wuhan University Journal of Natural Sciences,2007,12(2):203-206. |
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| Authors: | Su Dan Zhang Dunmu |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China;(2) School of Information Technology and Management Engineering, University of International Business and Economics, Beijing, 100029, China |
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| Abstract: | We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arrangement and the original hyperplane arangement. The Mobius function of the mixed arrangement is equal to the positive or the negative Mobius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement. |
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| Keywords: | mixed arrangement Mobius function characteristicpolynomial |
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