Mathematics – Combinatorics
Scientific paper
2009-03-16
Mathematics
Combinatorics
18 pages, 16 figures
Scientific paper
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.
Devadoss Satyan L.
Shah Rahul
Shao Xuancheng
Winston Ezra
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