On extremal point distributions in the Euclidean plane
Author: Pillichshammer F.
Source: Acta Mathematica Hungarica, Volume 98, Number 4, 2003 , pp. 311-321(11)
We ask for the maximum n of n i,j=1 ||xit-xj||, where x1, ,xn are points in the Euclidean plane R2 with ||x_i-x_j|| 1 for all 1 i,j n and where ||.|| denotes the -th power of the Euclidean norm, 1. (For =1 this question was stated by L. Fejes Tóth in .) We calculate the exact value of n for all 1,0758 and give the distributions which attain the maximum n. Moreover we prove upper bounds for n for all 1 and calculate the exact value of 4 for all 1.
Document Type: Research article
Publication date: 2003-01-01