Generaliation the result in our paper for sum and similarly my previous question for product. I have a question:
My question: Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?
Generaliation the result in our paper for sum and similarly my previous question for product. I have a question:
My question: Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?
This is actually an open problem, the only proven optimal configurations I have found are the universal configurations with N=1,2,3,4,6,12, and the dipyramid with N=5. Some work for N=7 is done here, which is compatible with this. Some bounds are given in the paper Sums of distances between points of a sphere.