Monotypical uniformly homogeneous sets of permutations (Q1203515)

Let \(S_ n\) denote the symmetric group on \(n\) letters. A subset \(S\) of \(S_ n\) is said to be \(\mu\)-uniformly \(t\)-homogeneous if exactly \(\mu\) elements of \(S\) map \(A\) to \(B\) where \(A,B\) are any two \(t\)-element subsets of the ground set. The main result of this paper deals with the determination of the conjugacy classes of \(S_ n\) which are uniformly \(t\)-homogeneous.