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Number of A+B\ne C solutions in abelian groups and application to counting independent sets in hypergraphs

European Journal of Combinatorics. 2022. Vol. 100. Article 103453.
Semchankau A., Shabanov D. A., Shkredov I.

The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order n. We investigate the number of subset triples (A,B,C) such that for any x from A, y from B, c from C x+y is not equal to z. We prove the tight estimate for this value. As a corollary, we provide a tight estimate for the number of independent sets in a special 3-uniform linear hypergraph and disproves the conjecture of Cohen et al. concerning the maximal possible number of independent sets in such hypergraphs on vertices.

Research target: Mathematics
Language: English
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DOI
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Keywords: abelian groupsdiscrete Fourier transformhypergraphs
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