16 citations · 39 across the 12 of their papers we have counts for
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math.CO2011
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…
math.CO2011★ 16 cited
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 $\…