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math.CO2018★ 8 cited
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
Polona Durcik, Vjekoslav Kovač
We prove that sets with positive upper Banach density in sufficiently large dimensions contain congruent copies of all sufficiently large dilates of three specific higher-dimension…
math.CO2016★ 17 cited
On side lengths of corners in positive density subsets of the Euclidean space
Polona Durcik, Vjekoslav Kovač, Luka Rimanić
We generalize a result by Cook, Magyar, and Pramanik [3] on three-term arithmetic progressions in subsets of to corners in subsets of $\mathbb{R}^d\times\mathbb{R}^d…