| 关于欧氏空间中超平面族的一个猜测 |
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| 引用本文： | 杨延龄. 关于欧氏空间中超平面族的一个猜测[J]. 北京工商大学学报(自然科学版), 1989, 0(1) |
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| 作者姓名： | 杨延龄 |
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| 作者单位： | 北京轻工业学院数学教研室 |
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| 摘 要： | 在欧氏空间R~n放置n个处于一般位置的超平面,由此而分割出的有界凸多面体的集记为{C_1,C_2…,C_r},用v(Ci)表示Ci的顶点个数。本文讨论数v(n,d)=min _i~(max){v(Ci)},这里的最小取遍所有可能的处于一般位置的放置。Kusner指出v(n,2)=4,n≥4,并猜测v(n,d)=2d,n≥2d≥2。本文证明这个猜测在d=3时不正确。
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| 关 键 词： | 放置 超平面 多面体 顶点 |
A CONJECTURE ON HYPERPLANES IN EUCLIDEAN SPACE |
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| Yang Yanling. A CONJECTURE ON HYPERPLANES IN EUCLIDEAN SPACE[J]. Journal of Beijing Technology and Business University:Natural Science Edition, 1989, 0(1) |
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| Authors: | Yang Yanling |
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| Affiliation: | Beijing Institute of Light Industry |
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| Abstract: | In Euclidean space R~d, let L_n= {A_j} be a family of n hyperplanes in general positions. Let C_1…, C_r be the bounded components of the complement of U A_j; v(C_i) is the number of the convex polytope C_i·Let v(L_n) =max/i {v(C_i)} andv(n, d) =min/L_n {v(L_n)}; minimum ts taken to cover all families L_n of n hyperplanes in general positions in R~d. R. Kusner posed a conjectore that v(n,d)=2d, for n2d2. ln this paper we prore that this conjecture is not true when d=3, and arrive at the following proposition: v(n,3)= 8, n6. |
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| Keywords: | arrangement hyperplane polyhydron vertex |
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