dc.contributor.author Freiman, Gregory A. dc.contributor.author Serra Albó, Oriol dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2018-12-17T11:15:24Z dc.date.available 2018-12-17T11:15:24Z dc.date.issued 2018-10-01 dc.identifier.citation Freiman, G., Serra, O. On doubling and volume: chains. "Acta Arithmetica", 1 Octubre 2018, vol. 186, núm. 1, p. 37-59. dc.identifier.issn 0065-1036(p) dc.identifier.uri http://hdl.handle.net/2117/125853 dc.description.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. dc.format.extent 23 p. dc.language.iso eng dc.publisher \Institute of Mathematics, Polish Academy of Sciences\ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres dc.subject.lcsh Sequences (Mathematics) dc.subject.lcsh Partitions (Mathematics) dc.subject.other additive number theory dc.subject.other sumsets dc.subject.other Freiman–Ruzsa theorem. dc.title On doubling and volume: chains dc.type Article dc.subject.lemac Successions (Matemàtica) dc.subject.lemac Particions (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics dc.identifier.doi 10.4064/aa170211-8-2 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::11 Number theory::11B Sequences and sets dc.subject.ams Classificació AMS::11 Number theory::11P Additive number theory; partitions dc.relation.publisherversion https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/186/1/112682/on-doubling-and-volume-chains dc.rights.access Open Access local.identifier.drac 23448209 dc.description.version Postprint (author's final draft) dc.relation.projectid info:eu-repo/grantAgreement/MINECO/1PE/MTM2014-54745-P dc.relation.projectid info:eu-repo/grantAgreement/MINECO/1PE/MDM-2014-0445 local.citation.author Freiman, G.; Serra, O. local.citation.publicationName Acta Arithmetica local.citation.volume 186 local.citation.number 1 local.citation.startingPage 37 local.citation.endingPage 59
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