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DCG
1999
13 years 7 months ago
1999
We show how to color the tiles in a heirarchical tiling system so that the resulting system is not only repetitive (i.e., has the local isomorphism property) but has prescribed col...
DCG
2006
13 years 7 months ago
2006
We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/13...
DCG
2007
13 years 7 months ago
2007
Any finite set X ⊂ Rd colored with d+3 2 colors, contains a rainbow subset Y ⊂ X, such that any ball that contains Y contains a positive fraction of the points of X. The bound...
DCG
2010
13 years 6 months ago
2010
Given any knot diagram E, we present a sequence of knot diagrams of the same knot type, for which the minimum number of Reidemeister moves required to pass to E is quadratic with ...
DCG
2008
13 years 7 months ago
2008
Abstract. We reformulate a known characterization of decomposability of polytopes in a way which may be more computationally convenient, and offer a more transparent proof. We appl...