Three identities between stirling numbers and the stabilizing character sequence

Let x denote the stabilizing character of the action of the finite group G on the finite set X. Let xk denote \G\-1ΣσEGx(σ)K. It is well known that xk is the number of orbits of the induced action of G on the Cartesian product X(k). We show if G is a least (k l)-fold transitive on X, then xk can be expressed in terms of Stirling numbers of both kinds. Three identities between Stirling numbers and the stabilizing character sequence are obtained. © 1976, American Mathematical Society