Finite k-Transversals of Infinite Families of Fat Convex Sets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| author_facet | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| contents | We prove an infinite $(p,q)$-theorem for piercing fat compact convex sets in $\RR^d$ with $k$-flats. Additionally, we develop a new framework through which infinite $(p,q)$-theorems concerning compact sets and $k$-flats can be extended to their 'colorful' variants. Further, we show that the existence of an infinite $(p,q)$-theorem does not necessarily imply the existence of the corresponding finite $(p,q)$-theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14091 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Finite k-Transversals of Infinite Families of Fat Convex Sets Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi Combinatorics Computational Geometry 52A35 G.2.m We prove an infinite $(p,q)$-theorem for piercing fat compact convex sets in $\RR^d$ with $k$-flats. Additionally, we develop a new framework through which infinite $(p,q)$-theorems concerning compact sets and $k$-flats can be extended to their 'colorful' variants. Further, we show that the existence of an infinite $(p,q)$-theorem does not necessarily imply the existence of the corresponding finite $(p,q)$-theorem. |
| title | Finite k-Transversals of Infinite Families of Fat Convex Sets |
| topic | Combinatorics Computational Geometry 52A35 G.2.m |
| url | https://arxiv.org/abs/2212.14091 |