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dc.contributor.authorFalconer, Kenneth
dc.contributor.authorKovač, Vjekoslav
dc.contributor.authorYavicoli, Alexia
dc.date.accessioned2021-10-19T14:30:01Z
dc.date.available2021-10-19T14:30:01Z
dc.date.issued2022-11-17
dc.identifier.citationFalconer , K , Kovač , V & Yavicoli , A 2022 , ' The density of sets containing large similar copies of finite sets ' , Journal d'Analyse Mathématique , vol. First Online . https://doi.org/10.1007/s11854-022-0231-6en
dc.identifier.issn0021-7670
dc.identifier.otherPURE: 269135153
dc.identifier.otherPURE UUID: cb498bc5-7ca8-42c1-84c0-db7499aedc15
dc.identifier.otherArXiv: http://arxiv.org/abs/2007.03493v1
dc.identifier.otherORCID: /0000-0001-8823-0406/work/123196745
dc.identifier.urihttp://hdl.handle.net/10023/24167
dc.descriptionFunding: VK is supported by the Croatian Science Foundation, project n◦ UIP-2017-05-4129 (MUNHANAP). AY is supported by the Swiss National Science Foundation, grant n◦ P2SKP2 184047.en
dc.description.abstractWe prove that if E⊆Rd (d≥2) is a Lebesgue-measurable set with density larger than n−2n−1, then E contains similar copies of every n-point set P at all sufficiently large scales. Moreover, 'sufficiently large' can be taken to be uniform over all P with prescribed size, minimum separation and diameter. On the other hand, we construct an example to show that the density required to guarantee all large similar copies of n-point sets tends to 1 at a rate 1−O(n−1/5log n).
dc.format.extent19
dc.language.isoeng
dc.relation.ispartofJournal d'Analyse Mathématiqueen
dc.subjectPatternen
dc.subjectDensityen
dc.subjectSimilarityen
dc.subjectArithmetic progressionen
dc.subjectDiscrepancyen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleThe density of sets containing large similar copies of finite setsen
dc.typeJournal articleen
dc.description.versionPreprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s11854-022-0231-6
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/2007.03493en


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