, Volume 170, Issue 2, pp 327-354
Date: 23 Aug 2007

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.