1 citations · 2 across the 4 of their papers we have counts for
4 papers
Computational Lower Bounds for Colourful Simplicial Depth
Antoine Deza, Tamon Stephen, Feng Xie
The colourful simplicial depth problem in dimension d is to find a configuration of (d+1) sets of (d+1) points such that the origin is contained in the convex hull of each set (col…
More Colourful Simplices
Antoine Deza, Tamon Stephen, Feng Xie
We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in \R^d is contained in at least (d+1)^2/2 simplices with one vertex from each s…
Hyperplane Arrangements with Large Average Diameter
Antoine Deza, Feng Xie
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds…
The complexity of the envelope of line and plane arrangements
David Bremner, Antoine Deza, Feng Xie
A facet of an hyperplane arrangement is called external if it belongs to exactly one bounded cell. The set of all external facets forms the envelope of the arrangement. The number…