Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915823866609664 |
|---|---|
| author | Alon, Noga Smorodinsky, Shakhar |
| author_facet | Alon, Noga Smorodinsky, Shakhar |
| contents | We prove a new Radon type theorem for unions of convex sets, settling an open problem posed by Kalai in the 1970s. We also define
and study an extension of the notion of the VC-dimension of a
hypergraph and apply it to establish an extension of our
Radon type theorem to a Tverberg type theorem
for unions of convex sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets Alon, Noga Smorodinsky, Shakhar Combinatorics Computational Geometry 52C10 We prove a new Radon type theorem for unions of convex sets, settling an open problem posed by Kalai in the 1970s. We also define and study an extension of the notion of the VC-dimension of a hypergraph and apply it to establish an extension of our Radon type theorem to a Tverberg type theorem for unions of convex sets. |
| title | Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets |
| topic | Combinatorics Computational Geometry 52C10 |
| url | https://arxiv.org/abs/2506.17777 |