We ask for the maximum σnγ of Σi,j=1n‖xi-xj‖γ, where x1,χ,xn are points in the Euclidean plane R2 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 .) We calculate the exact value of σnγ for all γ γ 1,0758χ and give the distributions which attain the maximum σnγ. Moreover we prove upper bounds for σnγ for all γ ≧ 1 and calculate the exact value of σ4γ for all γ ≧ 1.
Euclidean norm sum of distances
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