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dc.contributor.authorKolossváry, István
dc.identifier.citationKolossváry , I 2022 , ' An upper bound for the intermediate dimensions of Bedford–McMullen carpets ' , Journal of Fractal Geometry , vol. 9 , no. 1-2 , pp. 151-169 .
dc.identifier.otherPURE: 280827604
dc.identifier.otherPURE UUID: 799cc865-7d08-419d-a92b-20721dea62a2
dc.identifier.otherJisc: 520529
dc.identifier.otherORCID: /0000-0002-2216-305X/work/117211375
dc.identifier.otherWOS: 000835849700006
dc.descriptionThe author was supported by the Leverhulme Trust Research Project Grant RPG-2019-034.en
dc.description.abstractThe intermediate dimensions of a set Λ\LambdaΛ, elsewhere denoted by dim⁡θΛ\dim_{\theta}\Lambdadimθ​Λ, interpolate between its Hausdorff and box dimensions using the parameter θ∈[0,1]\theta\in[0,1]θ∈[0,1]. For a Bedford–McMullen carpet Λ\LambdaΛ with distinct Hausdorff and box dimensions, we show that dim⁡θΛ\dim_{\theta}\Lambdadimθ​Λ is strictly less than the box dimension of Λ\LambdaΛ for every θ<1\theta<1θ<1. Moreover, the derivative of the upper bound is strictly positive at θ=1\theta=1θ=1. This answers a question of Fraser; however, determining a precise formula for dim⁡θΛ\dim_{\theta}\Lambdadimθ​Λ still remains a challenging problem.
dc.relation.ispartofJournal of Fractal Geometryen
dc.rightsCopyright ©2022 European Mathematical Society. Published by EMS Press. Open Access. This work is licensed under a CC BY 4.0 licenseen
dc.subjectIntermediate dimensionsen
dc.subjectBedford-McMullen carpeten
dc.subjectHausdorff dimensionen
dc.subjectBox dimensionen
dc.subjectQA Mathematicsen
dc.titleAn upper bound for the intermediate dimensions of Bedford–McMullen carpetsen
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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