A point in the interior of the convex hulls
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910050153398272 |
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| author | Bárány, Imre Qi, Yun |
| author_facet | Bárány, Imre Qi, Yun |
| contents | Steinitz's theorem states that if a point $a \in \mathrm{int\,conv\,} X$ for a set $X \subset \mathbb{R}^d$, then $X$ contains a subset $Y$ of size at most $2d$ such that $a \in \mathrm{int\,conv\,}Y$. The bound $2d$ is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly $2d$ sets are needed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A point in the interior of the convex hulls Bárány, Imre Qi, Yun Combinatorics Steinitz's theorem states that if a point $a \in \mathrm{int\,conv\,} X$ for a set $X \subset \mathbb{R}^d$, then $X$ contains a subset $Y$ of size at most $2d$ such that $a \in \mathrm{int\,conv\,}Y$. The bound $2d$ is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly $2d$ sets are needed. |
| title | A point in the interior of the convex hulls |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.22907 |