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- W1508979458 abstract "We show that if $A$ and $B$ are finite sets of real numbers, then the number of triples $(a,b,c)in Atimes Btimes (Acup B)$ with $a+b=2c$ is at most $(0.15+o(1))(|A|+|B|)^2$ as $|A|+|B|toinfty$. As a corollary, if $A$ is antisymmetric (that is, $Acap(-A)=est$), then there are at most $(0.3+o(1))|A|^2$ triples $(a,b,c)$ with $a,b,cin A$ and $a-b=2c$. In the general case where $A$ is not necessarily antisymmetric, we show that the number of triples $(a,b,c)$ with $a,b,cin A$ and $a-b=2c$ is at most $(0.5+o(1))|A|^2$. These estimates are sharp." @default.
- W1508979458 created "2016-06-24" @default.
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- W1508979458 date "2012-11-28" @default.
- W1508979458 modified "2023-09-26" @default.
- W1508979458 title "Solving $apm b=2c$ in the elements of finite sets" @default.
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- W1508979458 hasPublicationYear "2012" @default.
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