Permutation Statistics on Signed Permutation Groups

Jiang Zeng

Institut Camille Jordan, Université Claude Bernard Lyon-I, France

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 (des

_{G}, maj, ℓ_{G}, col) and (des_{G}, ides_{G}, maj, imaj, col, icol) over the wreath product of a symmetric group by a cyclic group. Here des_{G}, ℓ_{G}, maj, col, ides_{G}, imaj_{G}, 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.