Finding
The resulting bounds are explicit and improve on the seminal result of Bourgain and Chang.
Paper
Query complexity and the polynomial Freiman–Ruzsa conjecture
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.
Authors
Dmitrii Zhelezov, Domotor P'alvolgyi
Journal
Advances in Mathematics
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