Large sets avoiding linear patterns

DOI10.1090/PROC/13959zbMATH Open1493.28009arXiv1706.08118OpenAlexW2963794974MaRDI QIDQ5012086

Alexia Yavicoli

Publication date: 31 August 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Abstract: We prove that for any dimension function $h$ with $hprec{x}^d$ and for any countable set of linear patterns, there exists a compact set $E$ with $mathcal{H}^h(E)>0$ avoiding all the given patterns. We also give several applications and recover results of Keleti, Maga, and M'{a}th'{e}.

Full work available at URL: https://arxiv.org/abs/1706.08118

zbMATH Keywords

Hausdorff dimensiondimension functionarithmetic progressionspatterns

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Fractals (28A80) Arithmetic progressions (11B25) Hausdorff and packing measures (28A78)

Cites Work

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Related Items (10)

Intersections of thick compact sets in \(\mathbb{R}^d\) ⋮ Large subsets of Euclidean space avoiding infinite arithmetic progressions ⋮ Full dimensional sets without given patterns ⋮ Large sets avoiding Infinite arithmetic / geometric progressions ⋮ Title not available (Why is that?) ⋮ Large sets containing no copies of a given infinite sequence ⋮ Large sets avoiding patterns ⋮ Sets of large dimension not containing polynomial configurations ⋮ Small sets containing any pattern ⋮ Patterns in thick compact sets

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