Name
Abstract | ||
|---|---|---|
Inspired by Barany's Colourful Caratheodory Theorem (4), we introduce a colourful generalization of Liu's simplicial depth (13). We prove a parity property and con- jecture that the minimum colourful simplicial depth of any core point in any d-dimensional configuration is d 2 + 1 and that the maximum is d d+1 + 1. We exhibit configurations attain- ing each of these depths, and apply our results to the problem of bounding monochrome (non-colourful) simplicial depth. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s00454-006-1233-3 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Computational Mathematic,Parity Property,Core Point,Simplicial Depth,Colourful Generalization | Topology,Combinatorics,Simplicial approximation theorem,Monochrome,Simplicial manifold,Simplicial complex,h-vector,Conjecture,Mathematics,Bounding overwatch | Journal |
Volume | Issue | ISSN |
35 | 4 | 0179-5376 |
Citations | PageRank | References |
11 | 1.26 | 8 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antoine Deza | 1 | 106 | 25.41 |
| Sui Huang | 2 | 21 | 2.02 |
| Tamon Stephen | 3 | 121 | 16.03 |
| Tamás Terlaky | 4 | 677 | 65.75 |