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Normal ordering in the -deformed generalized Weyl algebra. I: Algebraic Framework and Combinatorial Identities
Toufik Mansour, Lahcen Oussi, Matthias Schork
The -deformed generalized Weyl algebra is generated by variables and which satisfy the commutation relations , and ,…
Normal ordering in the -deformed generalized Weyl algebra. II: Interpretation in terms of rook placements
Toufik Mansour, Lahcen Oussi, Matthias Schork
In this paper, we investigate the combinatorial structure arising from the -deformed generalized Weyl algebra generated by variables , and , satisfying the $(p,…
Normal ordering in the -deformed generalized Weyl algebra. III: The binomial formula
Toufik Mansour, Lahcen Oussi, Matthias Schork
We study the -deformed generalized Weyl algebra generated by variables and satisfying the -commutation relations , and $…
A Poisson Type Operator Deformed by Generalized Fibonacci Numbers and Its Combinatorial Moment Formula
Nobuhiro Asai, Marek Bożejko, Lahcen Oussi +1
We introduce a two-parameter deformation of the classical Poisson distribution from the viewpoint of noncommutative probability theory, by defining a -Poisson type operator…
Analogues of Poisson type limit theorems in discrete bm-Fock spaces
Lahcen Oussi, Janusz Wysoczański
We present analogues of the Poisson limit distribution for the noncommutative bm-independence, which is associated with several positive symmetric cones. We construct related discr…
-analogues of the generalized Touchard polynomials and Stirling numbers
Lahcen Oussi
In this paper we introduce a -deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the -deformed generalized To…