Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.8

q-Derangement Identities

Emanuele Munarini
Dipartimento di Matematica
Politecnico di Milano
Piazza Leonardo da Vinci 32


In this paper, we derive several combinatorial identities involving the q-derangement numbers (for the major index) and many other q-numbers and q-polynomials of combinatorial interest, such as the q-binomial coefficients, the q-Stirling numbers, the q-Bell numbers, the q-Pochhammer symbol, the Gaussian polynomials, the Rogers-Szegő polynomials and the Galois numbers, and the Al-Salam-Carlitz polynomials. We also obtain two determinantal identities expressing the q-derangement numbers as tridiagonal determinants and as Hessenberg determinants.

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(Concerned with sequences A000110 A000166.)

Received October 27 2019; revised version received February 18 2020; March 11 2020. Published in Journal of Integer Sequences, March 17 2020.

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