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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2307.09854 |
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| _version_ | 1866909239985831936 |
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| author | Raigorodskii, Andrei M. Sagdeev, Arsenii |
| author_facet | Raigorodskii, Andrei M. Sagdeev, Arsenii |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09854 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on Borsuk's problem in Minkowski spaces Raigorodskii, Andrei M. Sagdeev, Arsenii Metric Geometry Combinatorics 52C10, 05D10, 51K05 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. |
| title | A note on Borsuk's problem in Minkowski spaces |
| topic | Metric Geometry Combinatorics 52C10, 05D10, 51K05 |
| url | https://arxiv.org/abs/2307.09854 |