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17

DCG
2011

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More Colourful Simplices

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More Colourful Simplices

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We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each set. This improves the known lower bounds for all d ≥ 4. Keywords Colourful simplicial depth · Colourful Carathéodory theorem · Discrete geometry

Antoine Deza, Tamon Stephen, Feng Xie

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Colourful Simplicial Depth | Computer Graphics | Convex Hull | DCG 2011 | Lower Bounds |

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Added	14 May 2011
Updated	14 May 2011
Type	Journal
Year	2011
Where	DCG
Authors	Antoine Deza, Tamon Stephen, Feng Xie

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