Geodesic
Avoiding maximal parabolic subgroups of S_k
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 1.

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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. 
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     author = {Mansour, Toufik and Vainshtein, Alek},
     title = {Avoiding maximal parabolic subgroups of {S_k}},
     journal = {Discrete mathematics & theoretical computer science},
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Mansour, Toufik; Vainshtein, Alek. Avoiding maximal parabolic subgroups of S_k. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 1. doi : 10.46298/dmtcs.276. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.276/

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