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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.
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]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Fernández%2C+Antonio%22">Fernández, Antonio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> antonio.fernandezg97@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Santos%2C+Francisco%22">Santos, Francisco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> francisco.santos@unican.es</i>
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  Data: 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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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00454-025-00738-1
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              Text: Jul2025
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