44 citations · 279 across the 33 of their papers we have counts for
4 papers · 2 filters
Unit Distances in Three Dimensions
Haim Kaplan, Jiri Matousek, Zuzana Safernova +1
We show that the number of unit distances determined by n points in R^3 is O(n^{3/2}), slightly improving the bound of Clarkson et al. established in 1990. The new proof uses the r…
Simple Proofs of Classical Theorems in Discrete Geometry via the Guth--Katz Polynomial Partitioning Technique
Haim Kaplan, Jiří Matoušek, Micha Sharir
Recently Guth and Katz \cite{GK2} invented, as a step in their nearly complete solution of Erdős's distinct distances problem, a new method for partitioning finite point sets in $\…
On Gromov's Method of Selecting Heavily Covered Points
Jiří Matoušek, Uli Wagner
A result of Boros and Füredi () and of Bárány (arbitrary ) asserts that for every there exists such that for every -point set , some point of…
The determinant bound for discrepancy is almost tight
Jiri Matousek
In 1986 Lovasz, Spencer, and Vesztergombi proved a lower bound for the hereditary a discrepancy of a set system F in terms of determinants of square submatrices of the incidence ma…