The number of permutations with given cycle structure and descent set is shown to be equal to the scalar product of two special characters of the symmetric group. Enumerative applications are given to cycles, involutions and derangements.
Gessel and Reutenauer REF showed that the number of permutations with given cycle structure and descent set can be expressed as a product of certain characters of the symmetric group.
Counting permutations with given cycle structure and descent set
J. Comb. Theory, Ser. A
J. Comb. Theory, Ser. A
Mathematics Computer Science