Lawrence Oriented Matroids and a Problem of McMullen on Projective Equivalences of Polytopes
Lawrence Oriented Matroids and a Problem of McMullen on Projective Equivalences of Polytopes
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劳伦斯定向拟阵和麦克马伦多面体射影等价问题
DOI：
10.1006/eujc.2000.0492
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. R. Alfonsín
中科院分区：
文献类型：
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作者：
J. R. Alfonsín
考虑McMullen提出的以下问题：确定最大整数n =f（d），使得在仿射d -空间Rd中一般位置的任何n个点的集合都可以通过投影变换映射到凸多面体的顶点上。据了解，2 d+ 1？f（d）<（d+ 1）（d+ 2）/2，证明了f（d）= 2d + 1.本文证明了f（d）<2d+？d+12？通过使用上述问题的众所周知的定向拟阵推广。
Consider the following question introduced by McMullen: Determine the largest integern=f(d) such that any set of n points in general position in the affine d -space Rdcan be mapped by a projective transformation onto the vertices of a convex polytope. It is known that 2 d+ 1 ?f(d) < (d+ 1)(d+ 2)/2 and it is conjectured that f(d) = 2 d+ 1. In this paper, we show that f(d) < 2 d+ ?d+1 2 ? by using a well-known oriented matroid generalization of the above problem.