The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n chessboard is n. This arrangement is achieved by placing the rooks along the diagonal. The total number of ways of placing n nonattacking rooks on an n×n board is n!. In general, the polynomial R_(m n)(x) = sum_k r_k^(m, n) x^k whose coefficients r_k^(m, n) give the numbers of ways k nonattacking rooks can be placed on an m×n chessboard is called a rook polynomial.

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