论文标题
抗逆转三角剖分的组合
Combinatorics of antiprism triangulations
论文作者
论文摘要
抗逆转三角剖分提供了一种自然的方法来细分简单的复杂$δ$，类似于Barycentric Subdivision，该细分在组合代数拓扑和计算机科学中独立出现。从组合的角度来看，它可以定义为$Δ$的多点面孔链的简单复合物，从几何学的角度来看。 本文研究了与该三角剖分相关的列举不变性，例如在抗精神三角剖分下$ h $δ$的$ h $ vector，以及其stanley-reisner环的代数特性。除其他结果外，还表明，$ H $ - 单纯性的单纯性三角剖分是真正的，并且$δ$的抗逆转三角剖分对每一个可撒的复合物$δ$Δ$ able $ {\ Mathbb r} $具有几乎强的lefschetz属性。讨论了几个相关的开放问题。
The antiprism triangulation provides a natural way to subdivide a simplicial complex $Δ$, similar to barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the simplicial complex of chains of multi-pointed faces of $Δ$, from a combinatorial point of view, and by successively applying the antiprism construction, or balanced stellar subdivisions, on the faces of $Δ$, from a geometric point of view. This paper studies enumerative invariants associated to this triangulation, such as the transformation of the $h$-vector of $Δ$ under antiprism triangulation, and algebraic properties of its Stanley--Reisner ring. Among other results, it is shown that the $h$-polynomial of the antiprism triangulation of a simplex is real-rooted and that the antiprism triangulation of $Δ$ has the almost strong Lefschetz property over ${\mathbb R}$ for every shellable complex $Δ$. Several related open problems are discussed.
