Rook theory has been investigated by many people since its introduction by Kaplansky and Riordan in 1946. Goldman, Joichi and White in 1975 showed that the sum over k of the product of the (n− k)-th… (More)

We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the q-case… (More)

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… (More)

1. Report on Barry Simon’s 70th Birthday Conferences 2. New edition of Beals & Wong: “Special Functions and Orthogonal Polynomials” 3. “WHAT IS... A Multiple Orthogonal Polynomial” in Notices of the… (More)

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… (More)

We introduce a combinatorial way of calculating the Hilbert series of bigraded Sn-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald… (More)

We prove a combinatorial formula for the Hilbert series of the Garsia-Haiman bigraded Sn-modules as weighted sums over standard Young tableaux in the hook shape case. This method is based on the… (More)