Rook numbers and the normal ordering problem

نویسنده

  • Anna Varvak
چکیده

Abstract. For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = ∑ ci,jU D . We demonstrate that the normal order coefficients ci,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 formula for the coefficients ci,j . We calculate the Weyl binomial coefficients: normal order coefficients of the element (D +U) in the Weyl algebra. We extend these results to the q-analogue of the Weyl algebra. We discuss further generalizations using i-rook numbers.

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 112  شماره 

صفحات  -

تاریخ انتشار 2005