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math.CO2026
Optimal lower bounds for epsilon-nets for lines in the plane
Ilay Hoshen, Wojciech Samotij
We prove that, for arbitrarily small positive , there is a finite planar point set such that every -net for the range space induced on by straight…
math.CO2024
Towards an optimal hypergraph container lemma
Marcelo Campos, Wojciech Samotij
The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asser…
math.CO2012
Independent sets in hypergraphs
József Balogh, Robert Morris, Wojciech Samotij
Many important theorems in combinatorics, such as Szemerédi's theorem on arithmetic progressions and the Erdős-Stone Theorem in extremal graph theory, can be phrased as statements…