On the oddness of percolation

Recently Mertens and Moore (2019 Phys. Rev. Lett. 123 230605) showed that site percolation 'is odd'. By this they mean that on an M × N square lattice the number of distinct site configurations that allow for vertical percolation is odd. We report here an alternative proof, based on recursive use of geometric symmetry, for both free and periodic boundary conditions. (letter)