2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74458We 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.10 pagesGroup TheoryCombinatoricsPrimary 20B30; Secondary 05C25, 05E15, 20C30, 20F69, 60C05, 68R05, 68R10text