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Symmetric Groups and Expanders

Martin Kassabov
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Abstract

We construct an explicit generating sets $F_n$ and $\tilde F_n$ of the alternating and the symmetric groups, which make the Cayley graphs $C(Alt(n), F_n)$ and $C(Sym(n), \tilde F_n)$ a family of bounded degree expanders for all sufficiently large $n$. These expanders have many applications in the theory of random walks on groups and other areas of mathematics.

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Martin Kassabov. 2005-03-10. Symmetric Groups and Expanders. https://arxiv.org/abs/math/0503204

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