1 citations · 1 across the 2 of their papers we have counts for
5 papers
Convexity, Elementary Methods, and Distances
Oliver Roche-Newton, Dmitrii Zhelezov
This paper considers an extremal version of the Erdős distinct distances problem. For a point set , let denote the set of all Euclidean distances dete…
A Weighted Prékopa-Leindler inequality and sumsets with quasicubes
Ben Green, Dávid Matolcsi, Imre Ruzsa +2
We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prékopa-Leindler inequality. This is then app…
An analytic approach to cardinalities of sumsets
Dávid Matolcsi, Imre Ruzsa, George Shakan +1
Let be a positive integer and finite. We study $$β(U) : = \inf_{\substack{A , B \neq \emptyset \\ \text{finite}}} \frac{|A+B+U|}{|A|^{1/2}{|B|^{1/2}}},…
On iterated product sets with shifts II
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
The main result of this paper is the following: for all there exists such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \s…
Bourgain-Chang's proof of the weak Erdős-Szemerédi conjecture
Dmitrii Zhelezov
This is an exposition of the following `weak' Erdős-Szemerédi conjecture for integer sets proved by Bourgain and Chang in 2004. For any there exists such that for…