q-deformed Ore-Stirling and Ore-Lah numbers are realized as mixed rook-file placements on the staircase and Laguerre boards respectively, with recurrences derived from the model and the construction extended to the polynomial Weyl algebra.
Viskov, Expansion in powers of a noncommutative binomial , Proc
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Rook theory, normal ordering in the $q$-deformed Ore algebra and the polynomial generalization
q-deformed Ore-Stirling and Ore-Lah numbers are realized as mixed rook-file placements on the staircase and Laguerre boards respectively, with recurrences derived from the model and the construction extended to the polynomial Weyl algebra.