Elliptic Rook and File Numbers
نویسندگان
چکیده
منابع مشابه
Elliptic Rook and File Numbers
Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel’s q-rook numbers by two additional independent parameters a and b, and a nome p. The elliptic rook numbers are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and ...
متن کاملRook numbers and the normal ordering problem
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 ....
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متن کاملp-Rook Numbers and Cycle Counting in Cp ≀ Sn
Cycle-counting rook numbers were introduced by Chung and Graham [7]. Cycle-counting q-rook numbers were introduced by Ehrenborg, Haglund, and Readdy [9] and cycle-counting q-hit numbers were introduced by Haglund [14]. Briggs and Remmel [4] introduced the theory of p-rook and p-hit numbers which is a rook theory model where the rook numbers correspond to partial permutations in Cp ≀ Sn, the wre...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6121