an:06470128
Zbl 1317.52018
Devadoss, Satyan L.; Shah, Rahul; Shao, Xuancheng; Winston, Ezra
Deformations of associahedra and visibility graphs
EN
Contrib. Discrete Math. 7, No. 1, 68-81 (2012).
00346959
2012
j
52B11 57Q10 68R05
visibility graph; associahedron; secondary polytope
Summary: Given an arbitrary polygon \(P\) with holes, we construct a polytopal complex analogous to the associahedron based on its convex diagonalizations of \(P\). This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a close cousin to the Carpenter's rule theorem of compitational geometry.