Intersection Patterns of Convex Sets

By Jirí Matousek. 2002

73 citations recorded by the source corpus.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2d4af616fcdef4c61310a0b067c9326d78d26149

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In Geometry and Topology

1. Martin Tancer

Citations in the corpus

• Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey (2011, background): “More importantly, Kalai and Meshulam [KM05] obtained a topological generalization (with a weaker conclusion, but still more general then that of Theorem 6.4).”
• A fractional Helly theorem for convex lattice sets (2003, unknown): “Let C1;y;Cn be convex sets in R such that T iAI Cia| for at least að n dþ1Þ index sets ID1⁄2n of size ðd þ 1Þ: Then there exists a point contained in at least bn of the Ci: The best possible value of bðd; aÞ is 1 ð1 aÞ1=ðdþ1Þ [7] and, in particular, b-1 as a-1: Alon et al.”