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ON q-DERANGEMENT NUMBERS AND POLYNOMIALS

Author

Listed:
  • 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)

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.

Suggested Citation

  • Taekyun Kim & Dae San Kim & Hye Kyung Kim, 2022. "ON q-DERANGEMENT NUMBERS AND POLYNOMIALS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-7, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402009
    DOI: 10.1142/S0218348X22402009
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