$\lambda$-Euler's Difference Table for Colored Permutations

Abstract

Motivated by the $\lambda$-Euler's difference table of  Eriksen et al. and colored Euler's difference table of Faliharimalala and Zeng,  we study the $\lambda$-analogue of colored Euler's difference table and generalize their results. We generalize the number of permutations with $k$-excedances studied by Liese and Remmel in colored permutations. We also extend Wang et al.'s recent results about $r$-derangements by relating with the sequences arising from the difference table.