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} }
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 (
References
SHOWING 1-2 OF 2 REFERENCES
On the expansion rate of Margulis expanders
- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 2006
- 7
- PDF