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math.CO2008
On rich lines in grids
Evan Borenstein, Ernie Croot
In this paper we show that if one has a grid A x B, where A and B are sets of n real numbers, then there can be only very few ``rich'' lines in certain quite small families. Indeed…
math.CO2008
On a certain generalization of the Balog-Szemeredi-Gowers Theorem
Ernie Croot, Evan Borenstein
In this note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due…
math.CO2008
A new proof of Roth's theorem on arithmetic progressions
Ernie Croot, Olof Sisask
We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of…