The correspondence discovered by Kunz and Wu (1978) between the site percolation problem and the multi-site Potts problem is extended to several lattices. It is found that the site percolation problem can be very simply formulated in terms of the operators used by Temperley and Lieb (1971). In three instances applying the dual transformation to these operators induces the matching transformation found by Sykes and Essam (1964) and it is conjectured that this may hold generally. It follows that site percolation problems, like bond percolation problems, depend on finding eigenvalues of row transfer operators.