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-Szegõ polynomials and the Galois numbers, and the Al-Salam-Carlitz polynomials. We also obtain two determinantal identities expressing the q-derangement numbers as tridiag-onal determinants and as Hessenberg determinants.

Q-derangement identities

E. Munarini
2020-01-01

Abstract

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-Szegõ polynomials and the Galois numbers, and the Al-Salam-Carlitz polynomials. We also obtain two determinantal identities expressing the q-derangement numbers as tridiag-onal determinants and as Hessenberg determinants.
2020
Combinatorial sum, Connection constant, q-Bell number, q-binomial sum, q-derangement number, q-exponential generating series, q-Stirling number
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1158703
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