Avoiding maximal parabolic subgroups of S k

Toufik Mansour, Alek Vainshtein
2000 Discrete Mathematics and Theoretical Computer Science   unpublished
We find an explicit expression for the generating function of the number of permutations in S n avoiding a subgroup of S k generated by all but one simple transpositions. The generating function turns out to be rational, and its denominator is a rook polynomial for a rectangular board.