Many regular triangulations and many polytopes
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n !)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an intermediate step, we show that certain neighborly polytop...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/208500 |
| Acceso en línea: | https://hdl.handle.net/2445/208500 |
| Access Level: | acceso abierto |
| Palabra clave: | Politops Geometria convexa Polytopes Convex geometry |
| Sumario: | We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n !)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an intermediate step, we show that certain neighborly polytopes (such as particular realizations of cyclic polytopes) have at least $(n !)^{\lfloor(d-1) / 2\rfloor \pm o(1)}$ regular triangulations. |
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