On Doubling and Volume: Chains

2016/08/17 by G. A. Freiman, Freiman, G. A., O. Serra +1
Mathematics · #05B10 #11B13 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05B10 #msc:11B13

paper · pdf · doi:10.48550/arxiv.1608.04916

Some corrections to the above version are included

arxiv created 2017/01/17 · arxiv updated 2017/01/18

Abstract

The well--known Freiman--Ruzsa Theorem provides a structural description of a set A of integers with |2A|≤ c|A| as a subset of a d--dimensional arithmetic progression P with |P|≤ 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.

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