Hollow polytopes with many vertices
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912344288788480 |
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| author | Arun, Srinivas Dillon, Travis |
| author_facet | Arun, Srinivas Dillon, Travis |
| contents | Given a set $S \subseteq \mathbb{R}^d$, a hollow polytope has vertices in $S$ but contains no other point of $S$ in its interior. We prove upper and lower bounds on the maximum number of vertices of hollow polytopes whose facets are simplices or whose vertices are in general position. We also obtain relatively tight asymptotic bounds for polytopes which do not contain lattice segments of large length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hollow polytopes with many vertices Arun, Srinivas Dillon, Travis Metric Geometry Given a set $S \subseteq \mathbb{R}^d$, a hollow polytope has vertices in $S$ but contains no other point of $S$ in its interior. We prove upper and lower bounds on the maximum number of vertices of hollow polytopes whose facets are simplices or whose vertices are in general position. We also obtain relatively tight asymptotic bounds for polytopes which do not contain lattice segments of large length. |
| title | Hollow polytopes with many vertices |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2504.17530 |