可见性图和伴随面体的变形
Visibility graphs and deformations of associahedra
摘要：
结合面体是一个凸多胞体，它的面偏序集是基于一个凸多边形的不相交对角线。给出了任意简单多边形P，基于P的凸对角化构造了一个类似于结合面体的多面体复形，描述了该复形的拓扑性质，并给出了基于次多面体的实现.此外，利用P的可见性图，创建了多边形的变形空间，该变形空间封装了结合面体的子结构。
英文摘要：
The associahedron is a convex polytope whose face poset is based on nonintersecting diagonals of a convex polygon. In this paper, given an arbitrary simple polygon P, we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P. We describe topological properties of this complex and provide realizations based on secondary polytopes. Moreover, using the visibility graph of P, a deformation space of polygons is created which encapsulates substructures of the associahedron.
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