Abstract
The q-differences of the generalized q-factorial of t of order n and increment h, at t = 0, are examined. These q-numbers are the coefficients of the expansion of the generalized q-factorial of t of order n and increment h into q-factorials of t with unit increment. A combinatorial interpretation of these coefficients as q-rook numbers of a constant jump Ferrers board is provided. Further, explicit expressions, recurrence relations, limiting expressions, orthogonality relation and other properties of these q-numbers are derived.
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