Symmetric Groups and Expanders

Details Symmetric Groups and Expanders Symmetric Groups and Expanders

2005-03-10

arxiv.org/abs/math/0503204v1

Mathematics

Group Theory

10 pages

Scientific paper

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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