Kusner's conjecture: Exact values and linear bounds

Hong-Jun Ge, Zixiang Xu, Yang Zhou

In 1983, Kusner conjectured that the largest equilateral set in ${\mathbb{R}}^n$ with metric ${\ell }_p$ has cardinality $n+1$ when $1<p<\infty$ and $2n$ when $p=1.$ This conjecture…