## Michael J. Schlosser and Meesue Yoo

# An elliptic extension of the general product formula
for augmented rook boards

### (21 pages)

**Abstract.**
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 rook numbers multiplied by the *k*-th
falling factorial polynomials factorize into a product.
In the sequel, different types of generalizations and analogues
of this product formula have been derived by various authors.
In 2008, Miceli and Remmel
constructed a rook theory model involving augmented rook boards
in which they showed the validity of a general product formula
which can be specialized to all other product formulas
that so far have appeared in the literature on rook theory.
In this work, we construct an elliptic extension of the
*q*-analogue of Miceli and Remmel's result. Special cases
yield elliptic extensions of various known rook theory models.

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