论文标题
简单复合物的均匀三角形的面部数量
Face numbers of uniform triangulations of simplicial complexes
论文作者
论文摘要
如果$ f $ f $ f $ fovector限制到$δ$的面孔仅取决于该面部的尺寸，则对简单复合物$δ$的三角剖分称为统一。 This paper proves that the entries of the $h$-vector of a uniform triangulation of $Δ$ can be expressed as nonnegative integer linear combinations of those of the $h$-vector of $Δ$, where the coefficients depend only on the dimension of $Δ$ and the $f$-vectors of the restrictions of the triangulation to simplices of various dimensions.此外，它提供了有关这些系数的信息，包括公式，复发关系和各种解释，并给出了一个均匀三角剖分的$ h $ polynomial的标准。这些结果统一并概括了有关特殊类型的三角形类型的文献，例如Barycentric，edgewise和间隔细分。
A triangulation of a simplicial complex $Δ$ is called uniform if the $f$-vector of its restriction to a face of $Δ$ depends only on the dimension of that face. This paper proves that the entries of the $h$-vector of a uniform triangulation of $Δ$ can be expressed as nonnegative integer linear combinations of those of the $h$-vector of $Δ$, where the coefficients depend only on the dimension of $Δ$ and the $f$-vectors of the restrictions of the triangulation to simplices of various dimensions. Moreover, it provides information about these coefficients, including formulas, recurrence relations and various interpretations, and gives a criterion for the $h$-polynomial of a uniform triangulation to be real-rooted. These results unify and generalize several results in the literature about special types of triangulations, such as barycentric, edgewise and interval subdivisions.
