2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59453We 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.Combinatorics05A05; 05A15; 05E35; 33C45text