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 ....
متن کاملRook Theory, Generalized Stirling Numbers and (p, q)-Analogues
In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...
متن کاملp-Rook Numbers and Cycle Counting in Cp o Sn
Cycle-counting rook numbers were introduced by Chung and Graham [8]. Cycle-counting q-rook numbers were introduced by Ehrenborg, Haglund, and Readdy [10] and cycle-counting q-hit numbers were introduced by Haglund [14]. Briggs and Remmel [5] 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 oSn, the wre...
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