Name: On doubling and volume: chains
Keywords: Partitions (Mathematics), Particions (Matemàtica), Mathematics - Number Theory, Classificació AMS::11 Number theory::11P Additive number theory; partitions, Classificació AMS::11 Number theory::11B Sequences and sets, 11B13, 05B10, Sequences (Mathematics), :11 Number theory::11P Additive number theory [Classificació AMS], Freiman–Ruzsa theorem, sumsets

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2018Embargo end date: 01 Jan 2016 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 186, pages 37-59 (issn: 0065-1036, eissn: 1730-6264,

Authors: Freiman, Gregory A.; Serra Albó, Oriol;

doi: 10.4064/aa170211-8-2 , 10.48550/arxiv.1608.04916

arXiv: http://arxiv.org/abs/1608.04916

handle: 2117/125853

On doubling and volume: chains

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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.

Some corrections to the above version are included

Related Organizations

Tel Aviv University
Israel
University of Barcelona
Spain
Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain

Keywords

Partitions (Mathematics), Particions (Matemàtica), Mathematics - Number Theory, Classificació AMS::11 Number theory::11P Additive number theory; partitions, Classificació AMS::11 Number theory::11B Sequences and sets, 11B13, 05B10, Sequences (Mathematics), :11 Number theory::11P Additive number theory [Classificació AMS], Freiman–Ruzsa theorem, sumsets, Classificació AMS::11 Number theory::11P Additive number theory, Successions (Matemàtica), partitions, FOS: Mathematics, Freiman–Ruzsa theorem., Mathematics - Combinatorics, additive number theory, :11 Number theory::11B Sequences and sets [Classificació AMS], Number Theory (math.NT), Combinatorics (math.CO), :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres

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