Michael J. Schlosser and Meesue Yoo
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 White and extended to the
q-case by Garsia and Remmel. We obtain similar results
for elliptic analogues of Garsia and Remmel's q-file numbers
for skyline boards.
We also provide an elliptic extension of the j-attacking model
introduced by Remmel and Wachs.
Various applications of our results include
elliptic analogues of (generalized) Stirling numbers of the first and
second kind, Lah numbers, Abel numbers, and r-restricted versions
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