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.

Keywords

• permutations
• forbidden patterns
• parabolic subgroups
• laguerre polynomials
• rook polynomials
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]