彩色单纯形深度
Colourful Simplicial Depth
摘要：
灵感来自Barany的丰富多彩的Caratheodory定理，我们介绍了一个丰富多彩的推广刘的单纯深度。我们证明了一个宇称性质，并猜想任何d维构型中任何核点的最小色单形深度是d ^2 +1，最大色单形深度是d^（d+1）+1。我们展示的配置达到这些深度，并将我们的结果的问题的边界单色（非彩色）单纯的深度。
英文摘要：
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.
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