Papers › Improved Exponent for Marton's Conjecture in 𝔽₂ⁿ
Improved Exponent for Marton's Conjecture in 𝔽₂ⁿ
Jyun-Jie Liao
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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=𝔽₂ⁿ. Specifically, for G=𝔽₂ⁿ, they proved that any set A⊆G with |A+A|≤K|A| can be covered by at most 2K^C cosets of a subgroup H of G of cardinality at most |A|, with C=12. In this paper we prove the same statement for C=9.
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