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Symmetric groups and expander graphs

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Abstract

We construct explicit generating sets S n 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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  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853-4201, USA

    Martin Kassabov

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  1. Martin Kassabov
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Correspondence to Martin Kassabov.

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Kassabov, M. Symmetric groups and expander graphs. Invent. math. 170, 327–354 (2007). https://doi.org/10.1007/s00222-007-0065-y

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