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98
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DCG
2008
15 years 13 days ago
2008
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness, and a lower bound. This imp...
DCG
2008
15 years 13 days ago
2008
The visibility graph V(X) of a discrete point set X R2 has vertex set X and an edge xy for every two points x, y X whenever there is no other point in X on the line segment betw...
64
Voted
DCG
2008
15 years 13 days ago
2008
We prove that for d 3, the 1-skeleton of any (d - 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette's lower b...
89
Voted
DCG
2008
15 years 13 days ago
2008
We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . In particular, we show that a family of n 2d disjoint unit balls in Rd has a line transversal if,...
107
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DCG
2008
15 years 13 days ago
2008
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that t...