Associahedra minimize $f$-vectors of secondary polytopes of planar point sets
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909653106950144 |
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| author | Fernández, Antonio Santos, Francisco |
| author_facet | Fernández, Antonio Santos, Francisco |
| contents | Kupavskii, Volostnov, and Yarovikov have recently shown that any set of $n$ points in general position in the plane has at least as many (partial) triangulations as the convex $n$-gon. We generalize this in two directions: we show that regular triangulations are enough, and we extend the result to all regular subdivisions, graded by the dimension of their corresponding face in the secondary polytope. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_00544 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Associahedra minimize $f$-vectors of secondary polytopes of planar point sets Fernández, Antonio Santos, Francisco Combinatorics 52C20, 52B05, 05C30 Kupavskii, Volostnov, and Yarovikov have recently shown that any set of $n$ points in general position in the plane has at least as many (partial) triangulations as the convex $n$-gon. We generalize this in two directions: we show that regular triangulations are enough, and we extend the result to all regular subdivisions, graded by the dimension of their corresponding face in the secondary polytope. |
| title | Associahedra minimize $f$-vectors of secondary polytopes of planar point sets |
| topic | Combinatorics 52C20, 52B05, 05C30 |
| url | https://arxiv.org/abs/2110.00544 |