A note on the affine plank conjecture
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918352898752512 |
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| author | Bakaev, Egor Yehudayoff, Amir |
| author_facet | Bakaev, Egor Yehudayoff, Amir |
| contents | In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in $\mathbb{R}^d$ is covered by planks, then the total relative width of the planks is at least one. We prove a lower bound of $2/(1+\sqrt{d})$ for this total relative width. The best previously known lower bound was $2/(1+d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the affine plank conjecture Bakaev, Egor Yehudayoff, Amir Metric Geometry 52A40 (Primary) 52C17 (Secondary) In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in $\mathbb{R}^d$ is covered by planks, then the total relative width of the planks is at least one. We prove a lower bound of $2/(1+\sqrt{d})$ for this total relative width. The best previously known lower bound was $2/(1+d)$. |
| title | A note on the affine plank conjecture |
| topic | Metric Geometry 52A40 (Primary) 52C17 (Secondary) |
| url | https://arxiv.org/abs/2602.20290 |