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<p>Kupavskii, Volostnov, and Yarovikov have recently shown that any set of <i>n</i> points in general position in the plane has at least as many (partial) triangulations as the convex <i>n</i>-gon. We generalize this in two directions: we show that <i>regular</i> triangulations are enough, and we extend the result to all regular subdivisions, graded by the dimension of their corresponding face in the secondary polytope.</p>

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Associahedra Minimize F-Vectors of Secondary Polytopes of Planar Point Sets

  • 期刊论文

  • 发表日期：

    2025年5月9日

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  • Antonio Fernández,
  • Francisco Santos

摘要

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.