摘要
令F表示平面上一个互不交紧凸集族。如果F的任何一个元素都不含于其它元素的并集的凸包中,则称F处于凸位置。如果F的任何三个元素都不共线,即对于F的任何三个元素,任两个元素的并集的凸包既不包含第三个元素也不与第三个元素互相交叉,则称F处于严格一般位置。对于处于严格一般位置的紧凸集族F,笔者改进了J.Pach和G.T幃th[5]以及赵永强[6]给出的P4(n)的上界,证明了P4(n)<(n-3)2+3,特别是用不同的方法还得到了另一个更好的结果P4(n)<nlog22n。
Let F denote a family of pairwise disjoint compact convex sets in the plane. F is said to be in convex position if none of its members is contained in the convex hull of the union of the others. F is said to be in strictly general position if no three members of F are collinear, i.e., for any three members of F, neither the convex hull of the union of two of them contains the third, nor the convex hull of the union of two of them and the third cross each other. For the family F which is in strictly general position, we improve the upper bound of P_4(n) provided by J. Pach and G. Tóth and show that P_4(n)<(n-3)~2+3. In particular, we get a much better result P_4(n)<n log_2 2n in a different way.
出处
《河北省科学院学报》
CAS
2004年第1期1-3,共3页
Journal of The Hebei Academy of Sciences
关键词
紧凸集
凸包
凸位置
严格一般位置
Compact convex set
Convex hull
Convex position
General position
Strictly general position
