OpenAlex ·
Kusner's conjecture is false for $p>4$
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.14794
- Original
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- Topics
Abstract
An equilateral set is a set of points in a metric space whose pairwise distances are all equal. Kusner conjectured that the maximum cardinality of an equilateral set in $\mathbb{R}^n$ with the $\ell_p$ metric is $n+1$ for every $14$. In particular, for every such $p$, we define $m=m(p)$ and construct an equilateral set of $8m$ points in $\mathbb{R}^{8m-2}$. Previously, Swanepoel disproved the conjecture for $1
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