A rook polynomial is a polynomial R_(m, n)(x) = sum_(k = 0)^(min(m, n)) r_k x^k whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook polynomials are given by R_(m, n)(x) = n!x^n L_n^(m - n)(-x^(-1)), where L_n^α(x) is an associated Laguerre polynomial.

rook number | rooks problem