A colorful Goodman-Pollack-Wenger theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909305157976064 |
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| author | Holmsen, Andreas F. |
| author_facet | Holmsen, Andreas F. |
| contents | Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals to general families of convex sets in $\mathbb{R}^d$ by Goodman, Pollack, and Wenger. Here we show a colorful genealization of their theorem which confirms a conjecture of Arocha, Bracho, and Montejano. The proof is topological and uses the Borsuk-Ulam theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04077 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A colorful Goodman-Pollack-Wenger theorem Holmsen, Andreas F. Combinatorics Metric Geometry Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals to general families of convex sets in $\mathbb{R}^d$ by Goodman, Pollack, and Wenger. Here we show a colorful genealization of their theorem which confirms a conjecture of Arocha, Bracho, and Montejano. The proof is topological and uses the Borsuk-Ulam theorem. |
| title | A colorful Goodman-Pollack-Wenger theorem |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2205.04077 |