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math.MG2022★ 4 cited
The density of planar sets avoiding unit distances
Gergely Ambrus, Adrián Csiszárik, Máté Matolcsi +2
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances cannot exc…
math.MG2022
A generalization of Bang's lemma
Gergely Ambrus
We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carathéodory Theorem. We also formulate a generalized version of the affi…