Subdivisions of Hypersimplices: with a View Toward Finite Metric Spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913245507354624 |
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| author | Casabella, Laura Joswig, Michael Kastner, Lars |
| author_facet | Casabella, Laura Joswig, Michael Kastner, Lars |
| contents | The secondary fan $Σ(k,n)$ is a polyhedral fan which stratifies the regular subdivisions of the hypersimplices $Δ(k,n)$. We find new infinite families of rays of $Σ(k,n)$, and we compute the fans $Σ(2,7)$ and $Σ(3,6)$. In the special case $k=2$ the fan $Σ(2,n)$ is closely related to the metric fan $\mathop{MF}(n)$, which forms a natural parameter space for the metric spaces on $n$ points. So our results yield a classification of the finite metric spaces on seven points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subdivisions of Hypersimplices: with a View Toward Finite Metric Spaces Casabella, Laura Joswig, Michael Kastner, Lars Combinatorics Metric Geometry 52B55, 52B11, 52B40, 05C12 The secondary fan $Σ(k,n)$ is a polyhedral fan which stratifies the regular subdivisions of the hypersimplices $Δ(k,n)$. We find new infinite families of rays of $Σ(k,n)$, and we compute the fans $Σ(2,7)$ and $Σ(3,6)$. In the special case $k=2$ the fan $Σ(2,n)$ is closely related to the metric fan $\mathop{MF}(n)$, which forms a natural parameter space for the metric spaces on $n$ points. So our results yield a classification of the finite metric spaces on seven points. |
| title | Subdivisions of Hypersimplices: with a View Toward Finite Metric Spaces |
| topic | Combinatorics Metric Geometry 52B55, 52B11, 52B40, 05C12 |
| url | https://arxiv.org/abs/2402.17665 |