The log-concavity of the q-derangement numbers of type B

Abstract

Abstract Recently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn (q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for D n B ( q ) $\begin{array}{} \displaystyle D^B_n(q) \end{array}$ discovered by Chow, we show that for n ≥ 4, the q-derangement numbers of type B D n B ( q ) $\begin{array}{} \displaystyle D^B_n(q) \end{array}$ are also log-concave.