On derangement polynomials of type B. II

Abstract

We define a type B derangement polynomial by q-counting derangements by the number of excedances in the hyperoctahedral group B n . Properties of the derangement polynomial, including the recurrence relation, generating function, real-rootedness, reciprocity and a unimodal decomposition arising from a symmetric function identity, are studied. The results presented generalize and unify earlier ones due to Brenti, Stanley, Stembridge and Zhang.