Large sets avoiding linear patterns
Classical Analysis and ODEs
2017-12-13 v5 Combinatorics
Metric Geometry
Abstract
We prove that for any dimension function with and for any countable set of linear patterns, there exists a compact set with avoiding all the given patterns. We also give several applications and recover results of Keleti, Maga, and M\'{a}th\'{e}.
Keywords
Cite
@article{arxiv.1706.08118,
title = {Large sets avoiding linear patterns},
author = {Alexia Yavicoli},
journal= {arXiv preprint arXiv:1706.08118},
year = {2017}
}
Comments
v5: small fixes and clarifications. To appear in Proceedings AMS