A counterexample to Kusner's conjecture on equilateral sets

Logan R. Chalmers

We disprove Kusner's 1983 conjecture that every equilateral set in ${\ell }_p^n$ with $2<p<\infty$ has at most $n+1$ points: there exist $58$ points in ${\mathbb{R}}^{56}$ whose pairwis…