3 edited tags
The symmetric group on $n$ letters has many sets of generators. Some of them are more natural than others, eg the set $(i,i+1)$ of adjacent transpositions (natural with respect to the type A Weyl group), the set of all shuffles and (permutations corresponding to "card-shuffles", ie $\sigma(1),\sigma(2),\dots,$ contains at most two increasing subsequences) perhaps also sets consisting of conjugacy classes (preferably of signature $-1$ in order to avoid a stupid mistake).
The symmetric group on $n$ letters has many sets of generators. Some of them are more natural than others, eg the set $(i,i+1)$ of adjacent transpositions, the set of all shuffles and perhaps also sets consisting of conjugacy classes (preferably of signature $-1$ in order to avoid a stupid mistake).