A block decomposition algorithm for computing rook polynomials
  Rook polynomials are a powerful tool in the theory of restricted permutations. It is known that the rook polynomial of any board can be computed recursively, using a cell decomposition technique of Riordan.   In this paper, we give a new decomposition theorem, which yields a more efficient algorithm for computing the rook polynomial. We show that, in the worst case, this block decomposition algorithm is equivalent to Riordan's method. 
Abigail G. Mitchell