Statistics on the Multi-Colored Permutation Groups

We define an excedance number for the multi-colored permutation group i.e. the wreath product (Zr1 × · · · × Zrk ) Sn and calculate its multi-distribution with some natural parameters. We also compute the multi-distribution of the parameters exc(π) and fix(π) over the sets of involutions in the multi-colored permutation group. Using this, we count the number of involutions in this group having a fixed number of excedances and absolute fixed points.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Eli Bagno, Ayelet Butman, David Garber
• Keywords: COMBINATORICS 2007, Excedance Number, Multi-colored Permutation Group, Wreath Product