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A quadratic lower bound for colourful simplicial depth

2005/12/16 by Tamon Stephen, Hugh Thomas, Stephen, Tamon +1
Computer Science · Engineering · Mathematics · #52A35 #52C45 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:52A35 #msc:52C45

paper · pdf · doi:10.48550/arxiv.math/0512400

4 pages, revised style and organization

openalex publication_date 2005/12/16 · arxiv created 2007/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any point in the convex hull of each of (d+1) sets of (d+1) points in Rd is contained in at least floor((d+2)2/4) simplices with one vertex from each set.

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