A Group Action on Derangements

Abstract

In this paper we define a cyclic analogue of the MFS-action on derangements, and give a combinatorial interpretation of the expansion of the $n$-th derangement polynomial on the basis $\{q^k(1 + q)^{n-1-2k}, k = 0, 1,... , \lfloor (n-1)/2\rfloor \}$.