Additive volume of sets contained in few arithmetic progressions
| dc.contributor.author | Freiman, Gregory A. |
| dc.contributor.author | Serra Albó, Oriol |
| dc.contributor.author | Spiegel, Christoph |
| dc.contributor.group | Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2023-09-07T08:13:28Z |
| dc.date.available | 2023-09-07T08:13:28Z |
| dc.date.issued | 2019-03-06 |
| dc.description.abstract | 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. |
| dc.description.peerreviewed | Peer Reviewed |
| dc.description.version | Postprint (published version) |
| dc.identifier.citation | Freiman, G.; Serra, O.; Spiegel, C. Additive volume of sets contained in few arithmetic progressions. "Integers (Berlin)", 6 Març 2019, vol. 19, núm. A34. |
| dc.identifier.issn | 1867-0660 |
| dc.identifier.other | https://arxiv.org/abs/1808.08455 |
| dc.identifier.uri | https://hdl.handle.net/2117/393204 |
| dc.language.iso | eng |
| dc.publisher | De Gruyter |
| dc.relation.projectid | 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/ |
| dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2014-54745-P/ES/ESTRUCTURAS DISCRETAS, GEOMETRICAS Y ALEATORIAS/ |
| dc.relation.publisherversion | http://math.colgate.edu/~integers/t34/t34.pdf |
| dc.rights.access | Open Access |
| dc.rights.licensename | Attribution-NonCommercial-NoDerivatives 4.0 International |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| dc.subject.ams | Classificació AMS::11 Number theory |
| dc.subject.ams | Classificació AMS::05 Combinatorics |
| dc.subject.lcsh | Number theory |
| dc.subject.lcsh | Combinatorial analysis |
| dc.subject.lemac | Nombres, Teoria dels |
| dc.subject.lemac | Combinacions (Matemàtica) |
| dc.subject.other | Number theory |
| dc.subject.other | Combinatorics |
| dc.title | Additive volume of sets contained in few arithmetic progressions |
| dc.type | Article |
| dspace.entity.type | Publication |
| local.citation.author | Freiman, G.; Serra, O.; Spiegel, C. |
| local.citation.number | A34 |
| local.citation.publicationName | Integers (Berlin) |
| local.citation.volume | 19 |
| local.identifier.drac | 35733893 |
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