Many regular triangulations and many polytopes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914765046022144 |
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| author | Padrol, Arnau Philippe, Eva Santos, Francisco |
| author_facet | Padrol, Arnau Philippe, Eva Santos, Francisco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01985 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Many regular triangulations and many polytopes Padrol, Arnau Philippe, Eva Santos, Francisco Combinatorics Metric Geometry 52B05 (Primary), 52B11 (Secondary) 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. |
| title | Many regular triangulations and many polytopes |
| topic | Combinatorics Metric Geometry 52B05 (Primary), 52B11 (Secondary) |
| url | https://arxiv.org/abs/2207.01985 |