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

The log-concavity of the q-derangement numbers of type B AbstractRecently, 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 forDnB(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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

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

Open Mathematics , Volume 16 (1): 6 – Feb 23, 2018

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Publisher
de Gruyter
Copyright
© 2018 Liu and Du, published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0009
Publisher site
See Article on Publisher Site

Abstract

AbstractRecently, 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 forDnB(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.

Journal

Open Mathematicsde Gruyter

Published: Feb 23, 2018

Keywords: The q -derangement numbers of type B; Unimodality; Log-concavity; 05A15; 05A19; 05A20

References