Symmetric groups and expander graphs

@article{Kassabov2005SymmetricGA,
  title={Symmetric groups and expander graphs},
  author={Martin Kassabov},
  journal={Inventiones mathematicae},
  year={2005},
  volume={170},
  pages={327-354}
}
  • M. Kassabov
  • Published 28 May 2005
  • Mathematics
  • Inventiones mathematicae
We construct explicit generating sets Sn and $\tilde{S}_{n}$ of the alternating and the symmetric groups, which turn the Cayley graphs $\mathcal{C}(\text{Alt}(n), S_{n})$ and $\mathcal{C}(\text{Sym}(n), \tilde{S}_{n})$ into a family of bounded degree expanders for all n. 
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