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

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 DnB(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 BDnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array}$ are also log-concave.

Keywords

• the q-derangement numbers of type b
• unimodality
• log-concavity
• 05a15
• 05a19
• 05a20