Polona Durcik

activity

20142026

most citedNorm-variation of ergodic averages with respect to two commuting transformations

22 citations · 105 across the 26 of their papers we have counts for

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3 papers · 1 filter

math.CO2022

Quantitative bounds for product of simplices in subsets of the unit cube

Polona Durcik, Mario Stipčić

For each $1 \leq i \leq n$ , let $k_{i} \geq 1$ and let $Δ_{i}$ be a set of vertices of a non-degenerate simplex of $k_{i} + 1$ points in $R^{k_{i} + 1}$ . If $A\subseteq [0,1]^{k_1+1}\tim…

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 $R^{d}$ to corners in subsets of $\mathbb{R}^d\times\mathbb{R}^d…