Improved Exponent for Marton's Conjecture in $\mathbb{F}_2^n$
Improved Exponent for Marton's Conjecture in $\mathbb{F}_2^n$
A conjecture of Marton, widely known as the polynomial Freiman-Ruzsa conjecture, was recently proved by Gowers, Green, Manners and Tao for any bounded-torsion Abelian group $G$. In this paper we show a few simple modifications that improve their bound in $G=\mathbb{F}_2^n$. Specifically, for $G=\mathbb{F}_2^n$, they proved that any set $A\subseteq …