A block decomposition algorithm for computing rook polynomials

Details A block decomposition algorithm for computing rook polynomials A block decomposition algorithm for computing rook polynomials

2004-06-30

arxiv.org/abs/math/0407004v1

Mathematics

Combinatorics

7 pages

Scientific paper

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.

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