摘要
本文研究了以下Heilbronn型问题:设S是欧氏空间按R^k 中由有限个点A_1,A_2,…,A_n组成的集合,令d(S)=min{A_iA_j|1≤i<j≤n},D(S)=max{A_iA_j|1≤i<j≤n},以及λ_(n,k)=min{D(S)/d(S)|S(?)R^k,|S|=n}.证明了下列结果:λ_(2k+2,2k)=(k+1)/k^(1/2),λ_(2k+1,2k-1)=((2k(k+1)/(2k^2-1))^(1/2))(k∈N),并讨论了λ_(n,k)的渐近性质.
The following problem of Heilbronn type is considered. Let S Rk be a set consists of n points A1, A2,…,An, d(S)=min{AiAj|1≤i<j≤n} and D(S) = max{AiAj|1≤i<j≤n}, and λn,κ=min{D(S)/d(S)|S Rk, |S|=n}.
We prove that
Meanwhile, we discuss the asymptotic behavior of λn,κ.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1997年第1期144-153,共10页
Acta Mathematica Sinica：Chinese Series
