On the number of antipodal or strictly antipodal pairs of points in finite subsets of ${\mathbb{R}}^d$, III

E. Makai, H. Martini, M. H. Nguyên +2

We improve our earlier upper bound on the numbers of antipodal pairs of points among $n$ points in ${\mathbb{R}}^3$, to $2n^2/5+O(n^c)$, for some $c<2$. We prove that the minimal n…