2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71745Rook 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.7 pagesCombinatorics05A05, 05A15 (Primary)text