The polynomial Freiman-Ruzsa conjecture in characteristic two

Let AF2nA\subset\mathbb{F}_{2}^{n} be a set with A+AKA|A+A|\leqslant K|A|. Polynomial Freiman-Ruzsa conjecture in characteristic two. Then AA is covered by at most 2KC2K^{C} cosets of some subgroup HF2nH\leqslant\mathbb{F}_{2}^{n} of size at most A|A|. This is presented as a characteristic-two version of the polynomial Freiman-Ruzsa conjecture; the source does not state its resolution status.

Sources & referencesView supporting material

Primary source

Weiwen Zhang, “Roth-type theorems in additive combinatroics”, arXiv:2512.08455 (2025).

Additional references

11 papers in this index state this conjecture (2004–2025). The statement above is taken from the most recent of them; the others are arXiv:2512.11217, arXiv:2312.08100, arXiv:2306.13403, arXiv:1403.8106, arXiv:1311.0172, arXiv:1301.7718, arXiv:1212.0458, arXiv:0906.3100, arXiv:0802.4371, arXiv:math/0409420.

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