Normal ordering in the -deformed generalized Weyl algebra. III: The binomial formula
arXiv:2607.11693
summary
The paper analyzes a (p,q)-deformed generalized Weyl algebra and derives a noncommutative binomial expansion (X+Y)^n, expressing the normal ordering coefficients via (p,q)-deformed s‑rook numbers.
Abstract
We study the -deformed generalized Weyl algebra generated by variables and satisfying the -commutation relations , and , with . Within this framework, we investigate the noncommutative binomial formula and related identities. In particular, we show how the associated normal ordering coefficients can be expressed in terms of -deformed -rook numbers. We treat several special cases explicitly, recovering known results from literature as well as deriving new ones.
36 pages
Topics & keywords
#deformed algebras#generalized Weyl algebra#normal ordering#noncommutative binomial formula#rook numbers(p,q)-deformation(p,q)-commutation relationss-rook numbersnormal ordering coefficientsnoncommutative binomial expansion