The number of faces of a simplicial convex polytope
The number of faces of a simplicial convex polytope
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DOI：
10.1016/0001-8708(80)90050-x
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发表时间：
1980-03
影响因子：
1.7
通讯作者：
R. Stanley
中科院分区：
文献类型：
--
作者：
R. Stanley
设P是具有fi= fi（P）维数为i的面的单纯凸d-多面体。向量f（P）=（f.，菲在1971年McMullen [6; 7，p.1791]中证明了向量f=（f.，菲fd...整数的J是f是某些单纯凸d-多胞形的f-向量的充要条件。Billera和Lee [1]证明了McMullen条件的充分性。在本文中，我们证明了必要性。从而完全验证了McMullen的猜想。
Let P be a simplicial convex d-polytope with fi= fi (P) faces of dimension i. The vector f (P)=(f., fi,..., fdel) is called the f-vector of P. In 1971 McMullen [6; 7, p. 1791 conjectured that a certain condition on a vector f=(f., fi,..., fd... J of integers was necessary and sufficient for f to be the f-vector of some simplicial convex d-polytope. Billera and Lee [l] proved the sufficiency of McMullen’s condition. In this paper we prove necessity. Thus McMullen’s conjecture is completely verified.