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Avoiding maximal parabolic subgroups of S_k

Abstract : 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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Toufik Mansour, Alek Vainshtein. Avoiding maximal parabolic subgroups of S_k. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2000, 4 (1), pp.81-90. ⟨hal-00958946⟩

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