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For an element w in the Weyl algebra generated by D and U with relation DU = U D + 1, the normally ordered form is w = c i,j U i D j. We demonstrate that the normal order coefficients c i,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit… (More)

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