Corpus ID: 119128141

A badly expanding set on the $2$-torus

@inproceedings{Ruhr2016ABE,
  title={A badly expanding set on the \$2\$-torus},
  author={Ren'e Ruhr},
  year={2016}
}

Ren'e Ruhr

Published 2016

Mathematics

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We give a counterexample to a conjecture stated in [LL06] regarding expansion on T2 under [ 1 1 0 1 ] and [ 1 0 1 1 ] . Let ΣD be the set containing the linear transformation σ1 = [ 1 1 0 1 ] and its transpose σ2 = [ 1 0 1 1 ], and let ΣU = ΣD ∪ Σ −1 D , adding the inverses of σ1 and σ2. Using these transformations, Linial and London [LL06] studied an infinite 4-regular expander graph, showing the following expansion property: For any bounded measurable set A ⊂ R of the plane, one has (1) m (