Big convex polytopes or rich hyperplanes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909627884503040 |
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| author | Furukawa, Koki |
| author_facet | Furukawa, Koki |
| contents | For natural numbers $n$ and $l > d \geq 2$, let $ES_d(l,n)$ be the minimum $N$ such that any set of at least $N$ points in $\mathbb{R}^d$ contains either $l$ points contained in a common $(d-1)$-dimensional hyperplane or $n$ points in convex position. In this paper, we give the upper and lower bounds for $ES_d(l,n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Big convex polytopes or rich hyperplanes Furukawa, Koki Combinatorics For natural numbers $n$ and $l > d \geq 2$, let $ES_d(l,n)$ be the minimum $N$ such that any set of at least $N$ points in $\mathbb{R}^d$ contains either $l$ points contained in a common $(d-1)$-dimensional hyperplane or $n$ points in convex position. In this paper, we give the upper and lower bounds for $ES_d(l,n)$. |
| title | Big convex polytopes or rich hyperplanes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.03645 |