## A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing

- Jacob Fox, János Pach, Andrew Suk
- SIAM J. Comput.
- 2016

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@article{Karasev2012ASP, title={A Simpler Proof of the Boros-F{\"u}redi-B{\'a}r{\'a}ny-Pach-Gromov Theorem}, author={Roman N. Karasev}, journal={Discrete & Computational Geometry}, year={2012}, volume={47}, pages={492-495} }

- Published 2012 in Discrete & Computational Geometry
DOI:10.1007/s00454-011-9332-1

A short and almost elementary proof of the Boros–Füredi–Bárány–Pach– Gromov theorem on the multiplicity of covering by simplices in R d is given. Let us give a proof of the Boros–Füredi–Bárány–Pach–Gromov theorem [1, 4, 8, 6] that is actually the " decoded " and refined proof from [6] (see also [5, Section 2] for a similar proof in the two-dimensional case). Unlike the proof in [6], the only topological notion that is used here is the degree of a piece-wise smooth map. Consider a set of d + 1… CONTINUE READING

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