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arXiv · 2307.09854

A note on Borsuk's problem in Minkowski spaces

Andrei M. Raigorodskii·Arsenii Sagdeev
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Abstract

In 1993, Kahn and Kalai famously constructed a sequence of finite sets in $d$-dimensional Euclidean spaces that cannot be partitioned into less than $(1.203\ldots+o(1))^{\sqrt{d}}$ parts of smaller diameter. Their method works not only for the Euclidean, but for all $\ell_p$-spaces as well. In this short note, we observe that the larger the value of $p$, the stronger this construction becomes.

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Andrei M. Raigorodskii, Arsenii Sagdeev. 2023-07-19. A note on Borsuk's problem in Minkowski spaces. https://doi.org/10.1134/s1064562424701849

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