Discrete Mathematics & Theoretical Computer Science

DMTCS

Volume 4 n° 1 (2000), pp. 67-77


author:Toufik Mansour and Alek Vainshtein
title:Avoiding maximal parabolic subgroups of Sk
keywords:permutations, forbidden patterns, parabolic subgroups, Laguerre polynomials, rook polynomials
abstract:We find an explicit expression for the generating function of the number of permutations in Sn avoiding a subgroup of Sk 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.
reference: Toufik Mansour and Alek Vainshtein (2000), Avoiding maximal parabolic subgroups of Sk, Discrete Mathematics and Theoretical Computer Science 4, pp. 67-77
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