A simpler proof of the Boros-Füredi-Bárány-Pach-Gromov theorem

DOI10.1007/s00454-011-9332-1zbMath1237.05054arXiv1012.5890OpenAlexW2067339112MaRDI QIDQ411397

Roman N. Karasev

Publication date: 4 April 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5890

zbMATH Keywords

simplicial depthmultiplicity of map

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Planar graphs; geometric and topological aspects of graph theory (05C10) Convex sets in (2) dimensions (including convex curves) (52A10)

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Cites Work

• Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
• On a notion of data depth based on random simplices
• The number of triangles covering the center of an \(n\)-set
• A generalization of Caratheodory's theorem
• The colored Tverberg's problem and complexes of injective functions
• A Tverberg-type result on multicolored simplices
• Optimal bounds for the colored Tverberg problem
• Overlap properties of geometric expanders
• A Colored Version of Tverberg's Theorem