On doubling and volume: chains
Volume 186 / 2018
Acta Arithmetica 186 (2018), 37-59
MSC: 11P70, 11B75.
DOI: 10.4064/aa170211-8-2
Published online: 12 October 2018
Abstract
The well-known Freiman–Ruzsa theorem provides a structural description of a set $A$ of integers with $|2A|\le c|A|$ as a subset of a $d$–dimensional arithmetic progression $P$ with $|P|\le c’|A|$, where $d$ and $c’$ depend only on $c$. The estimation of the constants $d$ and $c’$ involved in the statement has been the object of intense research. Freiman conjectured in 2008 a formula for the largest volume of such a set. In this paper we prove the conjecture for a general class of sets called chains.
