Colourful Simplicial Depth

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dc.creatorDeza, Antoine
dc.creatorHuang, Sui
dc.creatorStephen, Tamon
dc.creatorTerlaky, Tamás
dc.date2005-06-01
dc.date2006-01-08
dc.date.accessioned2026-07-07T06:40:09Z
dc.date.available2026-07-07T06:40:09Z
dc.descriptionInspired 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.
dc.description18 pages, 5 figues. Minor polishing
dc.identifierhttps://arxiv.org/abs/math/0506003
dc.identifierhttp://arxiv.org/abs/math/0506003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101322
dc.subjectCombinatorics
dc.subject52C45, 52A35
dc.titleColourful Simplicial Depth
dc.typetext

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