Jiang Zeng, Permutation Statistics on Signed Permutation Groups

Permutation Statistics on Signed Permutation Groups
Jiang Zeng
Institut Camille Jordan, Université Claude Bernard Lyon-I, France
2011/10/19 Wed 4PM-5PM (Room 3433)
We generalize two bijections due to Garsia and Gessel to compute the generating functions of the two vector statistics (desG, maj, ℓG, col) and (desG, idesG, maj, imaj, col, icol) over the wreath product of a symmetric group by a cyclic group. Here desG, ℓG, maj, col, idesG, imajG, and icol denote the number of descents, length, major index, color weight, inverse descents, inverse major index, and inverse color weight, respectively. Our main formulas generalize and unify several known identities due to Brenti, Carlitz, Chow-Gessel, Garsia-Gessel, and Reiner on various distributions of statistics over Coxeter groups of type A and B.


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