q-deformed Ore-Stirling numbers count mixed rook-file placements on staircase boards and q-deformed Ore-Lah numbers do the same on Laguerre boards, with the approach extended to polynomial commutation relations XY - qYX = f(Y).
Schork, Recent developments in combinatorial aspects of normal ordering , Enumer
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Rook theory, normal ordering in the $q$-deformed Ore algebra and the polynomial generalization
q-deformed Ore-Stirling numbers count mixed rook-file placements on staircase boards and q-deformed Ore-Lah numbers do the same on Laguerre boards, with the approach extended to polynomial commutation relations XY - qYX = f(Y).