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dc.contributor.authorBanaji, Amlan
dc.contributor.authorChen, Haipeng
dc.identifier.citationBanaji , A & Chen , H 2023 , ' Dimensions of popcorn-like pyramid sets ' , Journal of Fractal Geometry , vol. 10 , no. 1 , pp. 151-168 .
dc.identifier.otherPURE: 283533046
dc.identifier.otherPURE UUID: 9d6db8b9-07af-44d5-9ed6-14a127075a32
dc.identifier.otherORCID: /0000-0002-3727-0894/work/133726887
dc.identifier.otherScopus: 85169547864
dc.descriptionFunding: AB was financially supported by a Leverhulme Trust Research Project Grant (RPG-2019-034). HC was supported by NSFC (No. 11871227) and Shenzhen Science and Technology Program (Grant No. RCBS20210706092219049).en
dc.description.abstractThis article concerns the dimension theory of the graphs of a family of functions which include the well-known 'popcorn function' and its pyramid-like higher-dimensional analogues. We calculate the box and Assouad dimensions of these graphs, as well as the intermediate dimensions, which are a family of dimensions interpolating between Hausdorff and box dimension. As tools in the proofs, we use the Chung–Erdős inequality from probability theory, higher-dimensional Duffin–Schaeffer type estimates from Diophantine approximation, and a bound for Euler's totient function. As applications we obtain bounds on the box dimension of fractional Brownian images of the graphs, and on the Hölder distortion between different graphs.
dc.relation.ispartofJournal of Fractal Geometryen
dc.rightsCopyright © 2023 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license.en
dc.subjectPopcorn functionen
dc.subjectBox dimensionen
dc.subjectAssouad dimensionen
dc.subjectIntermediate dimensionsen
dc.subjectQA Mathematicsen
dc.titleDimensions of popcorn-like pyramid setsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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