论文标题
用2D + 2顶点的多面体边缘数量的最小数量
Minimum number of edges of polytopes with 2d + 2 vertices
论文作者
论文摘要
我们定义了立方体的类似物，并在较高的维度上定义了5-WEDGE的类似物，每个尺寸都有$ 2D+2 $顶点和$ d^2+2d-3 $边缘。我们表明，这两个是边缘数量的唯一最小化器，其中包括$ 2D+2 $ VERTICES的D-PolyTopes中，除了4、5和7外，所有$ d $。我们还表明，在这些低尺寸中，有四个零星的极小剂。我们宣布针对$ 2D + 3 $顶点的多面体问题的部分解决方案。
We define an analogue of the cube and an analogue of the 5-wedge in higher dimensions, each with $2d+2$ vertices and $d^2+2d-3$ edges. We show that these two are the only minimisers of the number of edges, amongst d-polytopes with $2d+2$ vertices, for all $d$ except 4, 5 and 7. We also show that there are four sporadic minimisers in these low dimensions. We announce a partial solution to the corresponding problem for polytopes with $2d + 3$ vertices.
