| Orlik-Solomon代数的NBC基的一个算法 |
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| 引用本文： | 章江华,姜广峰.Orlik-Solomon代数的NBC基的一个算法[J].北京化工大学学报(自然科学版),2005,32(1):85-89. |
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| 作者姓名： | 章江华 姜广峰 |
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| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
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| 基金项目： | 国家自然科学基金
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教育部留学回国人员科研启动基金 |
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| 摘 要： | 文中给出了Orlik-Solomon代数NBC基的一个算法，并在计算机上进行了实现。用此算法对顶点数小于7的带号完全n点形图构形做了π-分类，计算了各类的Poincaré多项式。最后，给出猜想“带号完全n点形的相反图构形A(G)是不自由的，则完全n点形图构形A(G)是自由的”的一个反例。
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| 关 键 词： | Orlik-Solomon代数 带号图构形 Poincare多项式 NBC基 |
| 收稿时间： | 2004-04-05 |
| 修稿时间： | 2004年4月5日 |
An algorithm about Orlik-Solomon algebra's NBC basis |
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| ZHANG Jiang,hua JIANG Guang,feng.An algorithm about Orlik-Solomon algebra's NBC basis[J].Journal of Beijing University of Chemical Technology,2005,32(1):85-89. |
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| Authors: | ZHANG Jiang hua JIANG Guang feng |
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| Institution: | College of Science, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | An algorithm for computing NBC basis of Orlik-Solomon algebra was given and implemented on a personal computer. The signed complementary graphic arrangements A(∑Kn) with n＜7 vertices were classified under π-equivalence, and the Poincaré polynomials of their representatives were worked out by this algorithm. Finally, a counter-example was addressed to a conjecture which says that if G and G(-) are not switching equivalent, then for all n≥4, A(G) is free if and only if A(G) is not free, where G is a complementary signed graph and G the negative graph of G. |
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| Keywords: | Orlik-Solomon algebra signed graphic arrangement Poincaré polynomial NBC basis |
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