On extremal point distributions in the Euclidean plane |
| |
Authors: | F Pillichshammer |
| |
Institution: | 1. Institut für Analysis, Universit?t, Linz Altenbergerstrasse 69, A-4040, Linz, Austria
|
| |
Abstract: | We ask for the maximum σ
n
γ
of Σ
i,j=1
n
‖x
i-x
j‖γ, where x
1,χ,x
n are points in the Euclidean plane R
2 with ‖xi-xj‖ ≦1 for all 1≦ i,j ≦ n and where ‖.‖γ denotes the γ-th power of the Euclidean norm, γ ≧ 1. (For γ =1 this question was stated by L. Fejes Tóth in 1].) We calculate
the exact value of σ
n
γ
for all γ γ 1,0758χ and give the distributions which attain the maximum σ
n
γ
. Moreover we prove upper bounds for σ
n
γ
for all γ ≧ 1 and calculate the exact value of σ
4
γ
for all γ ≧ 1.
This revised version was published online in June 2006 with corrections to the Cover Date. |
| |
Keywords: | Euclidean norm sum of distances |
本文献已被 SpringerLink 等数据库收录! |
|