ON q-DERANGEMENT NUMBERS AND POLYNOMIALS

Taekyun Kim (), Dae San Kim () and Hye Kyung Kim
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Taekyun Kim: Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Dae San Kim: Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Hye Kyung Kim: Department of Mathematics Education, Daegu Catholic University, Gyeongsan, Gyeongbuk 38430, Republic of Korea

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-7

Abstract: The derangement number dn is the number of fixed point free permutations on a set of n elements and the derangement polynomial dn(x) is a natural extension of the derangement number dn. The aim of this paper is to introduce q-derangement numbers and polynomials, which are q-analogs of the derangement numbers and polynomials, and to investigate their connection with some other q-special numbers and polynomials. In more detail, we derive explicit expressions and recurrence relations for the q-derangement numbers and polynomials. Further, we obtain some identities involving such polynomials and numbers and other special q-polynomials and numbers, which include q-Bell polynomials, q-analogs of Fubini polynomials and q-Stirling numbers of the second kind.

Keywords: q-Derangement Polynomials; q-Stirling Numbers of the Second Kind; q-Bell Polynomials; q-Analogs of Fubini Polynomials (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402009

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