k-维空间中n点确定的最大距离

The Maximum Distance Determined by n Points in k-dimensional Space

n点确定的不同距离问题是PErdos提出的重要问题。P是k-维空间的n元集,记P中两点确定的最大距离为dmax。Lenz给出4-维空间中,n点确定的最大距离可达n24次。现证明6-维空间中n点确定的最大距离可达n23次。在8-维空间中n点确定的最大距离可达3n28次。

The problem of different distances determined by a set of n points is a very important problem raised by P Erds.P is a set of n points in k-dimensioned space, the largest distance between two points in P is denoted as d_(max), which can occur as many times in 4-dimensional space asn^24. In this article, it is proved that in 6-dimensiond space it can occur as many times asn^23, and in 8-dimensiond space it can occurn^28 times.