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math.CA2019
On sets containing a unit distance in every direction
Pablo Shmerkin, Han Yu
We investigate the box dimensions of compact sets in that contain a unit distance in every direction (such sets may have zero Hausdorff dimension). Among other resul…
math.CA2019★ 1 cited
Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
Jonathan M. Fraser, Pablo Shmerkin, Alexia Yavicoli
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid -approximations of arithmetic progressions. Some of…