%0 Journal Article
%T A Note on Lower Bounds for Colourful Simplicial Depth
%A Antoine Deza
%A Tamon Stephen
%A Feng Xie
%J Symmetry
%D 2013
%I MDPI AG
%R 10.3390/sym5010047
%X 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, or colour, but contained in a minimal number of colourful simplices generated by taking one point from each set. A construction attaining d 2 + 1 simplices is known, and is conjectured to be minimal. This has been confirmed up to d = 3, however the best known lower bound for d ¡Ư 4 is £¿( d+1) 2 /2 £¿. In this note, we use a branching strategy to improve the lower bound in dimension 4 from 13 to 14.
%K colourful simplicial depth
%K Colourful Carath¨¦odory Theorem
%K discrete geometry
%K polyhedra
%K combinatorial symmetry
%U http://www.mdpi.com/2073-8994/5/1/47