A short and almost elementary proof of the Boros–Füredi–Bárány–Pach–Gromov theorem on the multiplicity of covering by simplices in ℝd is given.
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This research is supported by the Dynasty Foundation, grant MK-113.2010.1 of the President of Russian Federation, the Russian Foundation for Basic Research grants 10-01-00096 and 10-01-00139, the Federal Program “Scientific and scientific-pedagogical staff of innovative Russia” 2009–2013.
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Karasev, R. A Simpler Proof of the Boros–Füredi–Bárány–Pach–Gromov Theorem. Discrete Comput Geom 47, 492–495 (2012). https://doi.org/10.1007/s00454-011-9332-1
- Multiplicity of map
- Simplicial depth