Files in this item
Dimension growth for iterated sumsets
Item metadata
dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Howroyd, Douglas Charles | |
dc.contributor.author | Yu, Han | |
dc.date.accessioned | 2018-12-20T10:30:07Z | |
dc.date.available | 2018-12-20T10:30:07Z | |
dc.date.issued | 2018-12-17 | |
dc.identifier | 256914452 | |
dc.identifier | 8edea8c7-f860-4559-8401-811f1c2a54be | |
dc.identifier | 85058851244 | |
dc.identifier | 000495574800006 | |
dc.identifier.citation | Fraser , J , Howroyd , D C & Yu , H 2018 , ' Dimension growth for iterated sumsets ' , Mathematische Zeitschrift , vol. First Online . https://doi.org/10.1007/s00209-018-2224-9 | en |
dc.identifier.issn | 0025-5874 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285471 | |
dc.identifier.uri | https://hdl.handle.net/10023/16733 | |
dc.description | Jonathan 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.abstract | We 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.extent | 28 | |
dc.format.extent | 645102 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematische Zeitschrift | en |
dc.subject | Sumset | en |
dc.subject | Assouad dimension | en |
dc.subject | Box dimension | en |
dc.subject | Hausdorff dimension | en |
dc.subject | Distance set | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Dimension growth for iterated sumsets | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1007/s00209-018-2224-9 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2016-500 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.