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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