# The $q$-Stirling numbers of the second kind and its applications

Volume 11, Issue 8, pp 971--983 Publication Date: June 09, 2018       Article History
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### Authors

Min-Soo Kim - Division of Mathematics, Science, and Computers, Kyungnam University, 7(Woryeong-dong) kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do 51767, Republic of Korea. Daeyeoul Kim - Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-si 54896, Republic of Korea.

### Abstract

The study of $q$-Stirling numbers of the second kind began with Carlitz [L. Carlitz, Duke Math. J., $\textbf{15}$ (1948), 987--1000] in 1948. Following Carlitz, we derive some identities and relations related to $q$-Stirling numbers of the second kind which appear to be either new or else new ways of expressing older ideas more comprehensively.

### Keywords

• $q$-Stirling numbers of the second kind
• $q$-factorial

•  05A40
•  11A25

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