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math.CO2020
Maximal subsets free of arithmetic progressions in arbitrary sets
Aliaksei Semchankau
We consider the problem of determining the maximum cardinality of a subset containing no arithmetic progressions of length in a given set of size . It is proved that it is s…
math.CO2019★ 3 cited
On popular sums and differences of sets with small products
Konstantin I. Olmezov, Aliaksei S. Semchankau, Ilya D. Shkredov
Given a subset of real numbers with small product we obtain a new upper bound for the additive energy of . The proof uses a natural observation that level sets of convo…