Helly theorem for affine spaces without dimensions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866908677863112704 |
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| author | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| author_facet | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| contents | We prove a no-dimensional Helly theorem for affine spaces and convex sets using the unboundedness framework of Aronov, Goodman, and Pollack (Computational Geometry, 2002). This generalizes the fundamental result of Adiprasito, Bárány, Mustafa, and Terpai on the no-dimensional Helly theorem for points and convex sets (Discrete & Computational Geometry, 2020). Additionally, we establish the optimality of our result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10480 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Helly theorem for affine spaces without dimensions Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi Combinatorics Computational Geometry 52A35 We prove a no-dimensional Helly theorem for affine spaces and convex sets using the unboundedness framework of Aronov, Goodman, and Pollack (Computational Geometry, 2002). This generalizes the fundamental result of Adiprasito, Bárány, Mustafa, and Terpai on the no-dimensional Helly theorem for points and convex sets (Discrete & Computational Geometry, 2020). Additionally, we establish the optimality of our result. |
| title | Helly theorem for affine spaces without dimensions |
| topic | Combinatorics Computational Geometry 52A35 |
| url | https://arxiv.org/abs/2308.10480 |