3 citations · 8 across the 4 of their papers we have counts for
5 papers
Number of solutions in abelian groups and application to counting independent sets in hypergraphs
Aliaksei Semchankau, Dmitry Shabanov, Ilya Shkredov
The paper deals with a problem of Additive Combinatorics. Let be a finite abelian group of order . We prove that the number of subset triples $A,B,C\subset {\mathb…
A new bound for for large sets
Aliaksei Semchankau
For being a large prime number, and we prove the following: If does not cover all nonzero residues in , then $|A| < p/8 +…
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…
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…
On Differences of Multiplicative Functions and Solutions of the Equation
Aliaksei Semchankau
We will study the solutions to the equation , where and are multiplicative functions and is a constant. More precisely, we prove that the number of sol…