How to assemble rook polynomials?

Question

I have a problem. I need to assemble a rook polynomial for the chessboard (6x6 boards). Black boards are 1, white boards are 0.

                             1 1 1 1 0 0
                             1 1 1 0 0 0
                             1 1 0 0 1 1
                             1 1 0 1 1 1
                             0 0 1 1 1 1
                             0 0 1 1 1 1

Can anyone advise me or recommend me some literature, in which these problems are explained in detail? Thanks.

Answer 1

This is not a reference with detailed explanations, but if you want to quickly check your results, you can use this rook polynomial calculator. For the board that you describe above, it gives the rook polynomial $p(x)=1 + 24 x + 203 x^2 + 742 x^3 + 1158 x^4 + 648 x^5 + 76 x^6$ and calculates that only 4 of the 6! permutations will avoid the black squares.