Staircase polygons, scaling functions and asymmetric compact directed percolation

The scaling function for compact directed percolation on a square lattice is investigated for the asymmetric case where two parameters control the critical behaviour. A simple representation for the area-perimeter generating function for staircase polygons is found, which can be recast as a non-linear functional equation. From this, the exact scaling function is extracted. In the process, the most concise derivations to date are given for the exact low order cluster moments. (letter to the editor)