Logan R. Chalmers

collaborators

2 papers

math.MG2026

A counterexample to Kusner's conjecture on equilateral sets

Logan R. Chalmers

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

math.MG2026

A 32-leaf tree requiring six coordinates for an isometric $ℓ_{\infty}$ embedding

Logan R. Chalmers

We disprove the conjecture that every tree with t leaves embeds isometrically into $ℓ_{\infty}^{⌈ l o g_{2} t ⌉}$ . We construct a 32-leaf tree whose least isometric $\ell_\i…

A counterexample to Kusner's conjecture on equilateral sets

A 32-leaf tree requiring six coordinates for an isometric ℓ∞​ embedding

A 32-leaf tree requiring six coordinates for an isometric $ℓ_{\infty}$ embedding