On the excedance sets of colored permutations

Eli Bagno, David Garber, Robert Shwartz

Published 2008-06-12Version 1

We define the excedence set and the excedance word on $G_{r,n}$, generalizing a work of Ehrenborg and Steingrimsson and use the inclusion-exclusion principle to calculate the number of colored permutations having a prescribed excedance word. We show some symmetric properties as Log concavity and unimodality of a specific sequence of excedance words.