On Doubling and Volume: Chains

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 $|P|\le c^{\prime }|A|$, where $d$ and $c^{\prime }$ depend only on $c$. The estimation of the constants $d$ and $c^{\prime }$ 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.

Some corrections to the above version are included

References in corpus (1)

• On the Additive Volume of Sets of Integers

Cited by in corpus (1)

• Additive Volume of Sets Contained in Few Arithmetic Progressions