3 papers
math.CA2019
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…
math.CA2019
Patterns in thick compact sets
Alexia Yavicoli
We introduce a connection between Newhouse thickness and patterns through a variant of Schmidt's game introduced by Broderick, Fishman and Simmons. This yields an explicit, robust…
math.CA2017
Large sets avoiding linear patterns
Alexia Yavicoli
We prove that for any dimension function with and for any countable set of linear patterns, there exists a compact set with avoiding all…