The complex of non-crossing diagonals of a polygon |
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Authors: | Benjamin Braun Richard Ehrenborg |
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Affiliation: | Department of Mathematics, University of Kentucky, Lexington, KY, United States |
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Abstract: | Given a convex n-gon P in R2 with vertices in general position, it is well known that the simplicial complex θ(P) with vertex set given by diagonals in P and facets given by triangulations of P is the boundary complex of a polytope of dimension n−3. We prove that for any non-convex polygonal region P with n vertices and h+1 boundary components, θ(P) is a ball of dimension n+3h−4. We also provide a new proof that θ(P) is a sphere when P is convex with vertices in general position. |
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Keywords: | Non-convex polygon Associahedra Simplicial complex Discrete Morse theory |
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