Associahedra Minimize F-Vectors of Secondary Polytopes of Planar Point Sets.
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| Title: | Associahedra Minimize F-Vectors of Secondary Polytopes of Planar Point Sets. |
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| Authors: | Fernández, Antonio1 (AUTHOR) antonio.fernandezg97@gmail.com, Santos, Francisco1 (AUTHOR) francisco.santos@unican.es |
| Source: | Discrete & Computational Geometry. Jul2025, Vol. 74 Issue 1, p1-22. 22p. |
| Subjects: | Point set theory, Triangulation |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 01795376 |
| DOI: | 10.1007/s00454-025-00738-1 |
