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arXiv · 2606.03987

Kusner's conjecture: Exact values and linear bounds

Hong-Jun Ge·Zixiang Xu·Yang Zhou
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Abstract

In 1983, Kusner conjectured that the largest equilateral set in $\mathbb{R}^{n}$ with metric $\ell_{p}$ has cardinality $n+1$ when $1 2$, improving Alon's bounds $O_p(n^{2+\frac{2}{\lfloor p\rfloor}})$ for all finite $p\ge 1$.

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Hong-Jun Ge, Zixiang Xu, Yang Zhou. 2026-06-02. Kusner's conjecture: Exact values and linear bounds. https://arxiv.org/abs/2606.03987

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