Normal ordering coefficients in q-deformed generalized Ore algebras are interpreted as mixed rook and file placements on staircase and Laguerre boards, with extensions to polynomial Weyl algebras introducing associated q-deformed Stirling and Lah numbers.
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Normal ordering in the (p,q)-deformed generalized Weyl algebra yields (p,q)-deformed s-rook numbers that give combinatorial interpretations of (p,q)-generalized Stirling numbers on staircase boards.
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Rook theory, normal ordering in the $q$-deformed Ore algebra and the polynomial generalization
Normal ordering coefficients in q-deformed generalized Ore algebras are interpreted as mixed rook and file placements on staircase and Laguerre boards, with extensions to polynomial Weyl algebras introducing associated q-deformed Stirling and Lah numbers.
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Normal ordering in the $(p,q)$-deformed generalized Weyl algebra. II: Interpretation in terms of rook placements
Normal ordering in the (p,q)-deformed generalized Weyl algebra yields (p,q)-deformed s-rook numbers that give combinatorial interpretations of (p,q)-generalized Stirling numbers on staircase boards.