Abstract
The rook polynomial of a board counts the number of ways of placing nonattacking rooks on the board. In this paper, we describe how the properties of the two-dimensional rook polynomials generalize to the rook polynomials of “boards” in three and higher dimensions. We also define families of three-dimensional boards which generalize the two-dimensional triangle boards and the boards representing the probleme des rencontres. The rook coefficients of these threedimensional boards are shown to be related to famous number sequences such as the central factorial numbers, the number of Latin rectangles and the Genocchi numbers.
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