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arXiv · 2110.00544

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

Antonio Fernández·Francisco Santos
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Abstract

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.

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Antonio Fernández, Francisco Santos. 2025-05-09. Associahedra minimize $f$-vectors of secondary polytopes of planar point sets. https://doi.org/10.1007/s00454-025-00738-1

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