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- W3203995226 abstract "We prove a query complexity variant of the weak polynomial Freiman-Ruzsa conjecture in the following form. For any $epsilon > 0$, a set $A subset mathbb{Z}^d$ with doubling $K$ has a subset of size at least $K^{-frac{4}{epsilon}}|A|$ with coordinate query complexity at most $epsilon log_2 |A|$. We apply this structural result to give a simple proof of the few products, many sums phenomenon for integer sets. The resulting bounds are explicit and improve on the seminal result of Bourgain and Chang." @default.
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- W3203995226 date "2021-12-01" @default.
- W3203995226 modified "2023-10-18" @default.
- W3203995226 title "Query complexity and the polynomial Freiman–Ruzsa conjecture" @default.
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- W3203995226 doi "https://doi.org/10.1016/j.aim.2021.108043" @default.
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