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dc.contributor.authorFraser, Jonathan
dc.contributor.authorHowroyd, Douglas Charles
dc.contributor.authorYu, Han
dc.date.accessioned2018-12-20T10:30:07Z
dc.date.available2018-12-20T10:30:07Z
dc.date.issued2018-12-17
dc.identifier256914452
dc.identifier8edea8c7-f860-4559-8401-811f1c2a54be
dc.identifier85058851244
dc.identifier000495574800006
dc.identifier.citationFraser , J , Howroyd , D C & Yu , H 2018 , ' Dimension growth for iterated sumsets ' , Mathematische Zeitschrift , vol. First Online . https://doi.org/10.1007/s00209-018-2224-9en
dc.identifier.issn0025-5874
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285471
dc.identifier.urihttps://hdl.handle.net/10023/16733
dc.descriptionJonathan M. Fraser was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1). Douglas C. Howroyd was financially supported by the EPSRC Doctoral Training Grant (EP/N509759/1). Han Yu was financially supported by the University of St Andrews.en
dc.description.abstractWe study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set F⊆ℝ satisfies ^dim^BF+F>^dim^BF or even dimHnF→1. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors–David regular sets. Our proofs rely on Hochman’s inverse theorem for entropy and the Assouad and lower dimensions play a critical role. We give several applications of our results including an Erdős–Volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension.
dc.format.extent28
dc.format.extent645102
dc.language.isoeng
dc.relation.ispartofMathematische Zeitschriften
dc.subjectSumseten
dc.subjectAssouad dimensionen
dc.subjectBox dimensionen
dc.subjectHausdorff dimensionen
dc.subjectDistance seten
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleDimension growth for iterated sumsetsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1007/s00209-018-2224-9
dc.description.statusPeer revieweden
dc.identifier.grantnumberRF-2016-500en
dc.identifier.grantnumberEP/R015104/1en


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