Distributions of Points in d Dimensions and Large k-Point Simplices Eztended Abstract

摘要：

We consider a variant of Heilbronns triangle problem by asking for fixed dimension d≥2 and for fixed integers k≥3 with k≤d+ 1 for a distribution of n points in the d-dimensional unit-cube 0, 1d such that the minimum volume of a k-point simplex among these n points is as large as possible. Denoting by △k,d(n) the supremum of the minimum volume of a k-point simplex among n points over all distributions of n points in 0, 1d we will show that ck ·(log n)1/(d-k+2)/n(k-1)/(d-k+2)≤△k,d(n)≤ck/n(k-1)/d for 3≤k≤d+ 1, and moreover △k,d(n)≤ck/n(k-1)/d+(k-2)/(2d(d-1)) for k≥4 even, and constants ck,ck,ck > 0.

作者: Hanno Lefmann

作者单位: Fakultat fur Informatik, TU Chemnitz, D-09107 Chemnitz, Germany

会议类型: 国际会议

会议名称: The 11th Annual International Computing and Combinatorics Conference COCOON 2005(第11届国际计算和组合会议)

会议地点: 昆明

会议语种:英文

页码: 514-523

在线出版日期: 2005-08-01（万方平台首次上网日期，不代表论文的发表时间）