English

Large sets avoiding linear patterns

Classical Analysis and ODEs 2017-12-13 v5 Combinatorics Metric Geometry

Abstract

We prove that for any dimension function hh with hxdh \prec x^d and for any countable set of linear patterns, there exists a compact set EE with Hh(E)>0\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}.

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