Colourful Simplicial Depth
组合数学
2007-05-23 v3
摘要
Inspired by Barany's colourful Caratheodory theorem, we introduce a colourful generalization of Liu's simplicial depth. We prove a parity property and conjecture 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 attaining each of these depths and apply our results to the problem of bounding monochrome (non-colourful) simplicial depth.
引用
@article{arxiv.math/0506003,
title = {Colourful Simplicial Depth},
author = {Antoine Deza and Sui Huang and Tamon Stephen and Tamás Terlaky},
journal= {arXiv preprint arXiv:math/0506003},
year = {2007}
}
备注
18 pages, 5 figues. Minor polishing