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- W3207992364 abstract "The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order N. We prove that the number of subset triples A,B,C⊂G such that for any x∈A, y∈B and z∈C one has x+y≠z equals 3⋅4N+N3N+1+O((3−c∗)N) for some absolute constant c∗>0. This provides a tight estimate for the number of independent sets in a special 3-uniform linear hypergraph and disproves the conjecture of Cohen et al. (0000). concerning the maximal possible number of independent sets in such hypergraphs on n vertices." @default.
- W3207992364 created "2021-11-08" @default.
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- W3207992364 date "2022-02-01" @default.
- W3207992364 modified "2023-09-25" @default.
- W3207992364 title "Number of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e37 altimg=si11.svg><mml:mrow><mml:mi>A</mml:mi><mml:mo linebreak=goodbreak linebreakstyle=after>+</mml:mo><mml:mi>B</mml:mi><mml:mo linebreak=goodbreak linebreakstyle=after>≠</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math> solutions in abelian groups and application to counting independent sets in hypergraphs" @default.
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- W3207992364 doi "https://doi.org/10.1016/j.ejc.2021.103453" @default.
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