30 citations · 112 across the 24 of their papers we have counts for
25 papers
Large sets avoiding infinite arithmetic / geometric progressions
Alex Burgin, Samuel Goldberg, Tamás Keleti +2
We study some variants of the Erdős similarity problem. We pose the question if every measurable subset of the real line with positive measure contains a similar copy of an infinit…
Generic properties of topological groups
Márton Elekes, Boglárka Gehér, Tamás Kátay +3
We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. N…
Equivalences between different forms of the Kakeya conjecture and duality of Hausdorff and packing dimensions for additive complements
Tamás Keleti, András Máthé
The Kakeya conjecture is generally formulated as one the following statements: every compact/Borel/arbitrary subset of that contains a (unit) line segment in every…
Tiling of rectangles with squares via Diophantine approximation
Tamás Keleti, Stephen Lacina, Changshuo Liu +2
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor netwo…
Generic countably infinite groups
Márton Elekes, Boglárka Gehér, Kristóf Kanalas +2
Countably infinite groups (with a fixed underlying set) constitute a Polish space with a suitable metric, hence the Baire category theorem holds in . We study isomorphism in…
Hausdorff dimension of union of lines that cover a curve
Tamás Keleti, James Cumberbatch, Jialin Zhang
We construct a continuously differentiable curve in the plane that can be covered by a collection of lines such that every line intersects the curve at a single point and the union…