292 citations
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math.MG2019★ 8 cited
Assouad dimension influences the box and packing dimensions of orthogonal projections
Kenneth J. Falconer, Jonathan M. Fraser, Pablo Shmerkin
We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections…
math.MG2014★ 17 cited
Squares and their centers
Tamás Keleti, Dániel T. Nagy, Pablo Shmerkin
We study the relationship between the sizes of two sets when contains either the whole boundary, or the four vertices, of a square with axes-parallel…