Name
Abstract | ||
|---|---|---|
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 >= 4 is left perpendicular(d+1)(2)/2right perpendicular. In this note, we use a branching strategy to improve the lower bound in dimension 4 from 13 to 14. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.3390/sym5010047 | SYMMETRY-BASEL |
Keywords | DocType | Volume |
colourful simplicial depth,Colourful Caratheodory Theorem,discrete geometry,polyhedra,combinatorial symmetry | Journal | 5 |
Issue | ISSN | Citations |
1 | 2073-8994 | 0 |
PageRank | References | Authors |
0.34 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antoine Deza | 1 | 106 | 25.41 |
| Tamon Stephen | 2 | 121 | 16.03 |
| Feng Xie | 3 | 8 | 2.71 |