2026-04-17T04:12:09Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3932042025-07-17T04:39:31Zcom_2072_1033col_2072_452950

urn:hdl:2117/393204 Additive volume of sets contained in few arithmetic progressions Freiman, Gregory A. Serra Albó, Oriol Spiegel, Christoph Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria Number theory Combinatorial analysis Number theory Combinatorics Nombres, Teoria dels Combinacions (Matemàtica) Classificació AMS::11 Number theory Classificació AMS::05 Combinatorics A conjecture of Freiman gives an exact formula for the largest volume of a finite set A of integers with given cardinality k=|A| and doubling T=|2A|. The formula is known to hold when T=3k-4, for some small range over 3k-4 and for families of structured sets called chains. In this paper we extend the formula to sets of every dimension and prove it for sets composed of three segments, giving structural results for the extremal case. A weaker extension to sets composed of a bounded number of segments is also discussed. Peer Reviewed Postprint (published version) 2019-03-06 Article http://math.colgate.edu/~integers/t34/t34.pdf info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-82166-P/ES/COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA/ info:eu-repo/grantAgreement/MINECO//MTM2014-54745-P/ES/ESTRUCTURAS DISCRETAS, GEOMETRICAS Y ALEATORIAS/ http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International De Gruyter