A note on Borsuk's problem in Minkowski spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909239985831936 |
|---|---|
| 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 |