Colourful Simplicial Depth

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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.
18 pages, 5 figues. Minor polishing

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Combinatorics, 52C45, 52A35

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http://salesiana.dossiersoluciones.com/handle/123456789/101322

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506003
 http://arxiv.org/abs/math/0506003

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arXiv