Meshulam bound for cap sets
= Meshulam bound for cap sets
{c}
{title2=$|A|=O(3^n/n)$}
A <cap set> in $\mathbb F_3^n$ has <subset density> $O(1/n)$. A <Fourier analysis on a finite abelian group> proof uses a <hyperplane density increment for cap sets> repeatedly: absence of nondiagonal zero-sum triples forces a large <finite abelian Fourier coefficient>, and hence a denser slice. This is a weaker bound than the <Ellenberg–Gijswijt cap-set bound>, but illustrates the <density increment> method.