Deformations of associahedra and visibility graphs. (English) Zbl 1317.52018

Devadoss, Satyan L.; Shah, Rahul; Shao, Xuancheng; Winston, Ezra

Contrib. Discrete Math. 7, No. 1, 68-81 (2012).

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.

MSC:

52B11	\(n\)-dimensional polytopes
57Q10	Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
68R05	Combinatorics in computer science

Keywords:

visibility graph; associahedron; secondary polytope