Linear Conditions on the Number of Faces of Manifolds with Boundary
Linear Conditions on the Number of Faces of Manifolds with Boundary
复制标题
有边界流形面数的线性条件
DOI：
10.1006/aama.1997.0537
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发表时间：
1997
影响因子：
1.1
通讯作者：
M. Yan
中科院分区：
文献类型：
--
作者：
Beifang Chen;M. Yan
欧拉方程和德恩？Sommerville方程是球面三角剖分的f-向量（不同维数的单形数）唯一的（有理）线性条件。我们将这一事实推广到任意三角剖分，线性流形三角剖分，和多面体的欧氏球三角剖分。我们证明，闭流形，欧拉方程和德恩？Sommerville方程仍然是唯一的线性条件。我们还证明了对于非空边界的流形，欧拉方程是唯一的线性条件。这些结果不仅在Q上得到了证明，而且在Z和Z/kZ上也得到了证明。
The Euler equation and the Dehn?Sommerville equations are known to be the only (rational) linear conditions forf-vectors (number of simplices at various dimensions) of triangulations of spheres. We generalize this fact to arbitrary triangulations, linear triangulations of manifolds, and polytopal triangulations of Euclidean balls. We prove that for closed manifolds, the Euler equation and the Dehn?Sommerville equations remain the only linear conditions. We also prove that for manifolds with nonempty boundary, the Euler equation is the only linear condition. These results are proved not only over Q, but also over Z and Z/kZ.