Discrete & Computational Geometry

, Volume 35, Issue 4, pp 597–615 | Cite as

Colourful Simplicial Depth



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 d2 + 1 and that the maximum is dd+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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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1Canada
  2. 2.Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6Canada

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