Associahedra minimize $f$-vectors of secondary polytopes of planar point sets

Fuente: arXiv
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Main Authors: Fernández, Antonio, Santos, Francisco
Format: Preprint
Published: 2021
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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
id 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