Directed compact percolation near a wall: III. Exact results for the mean length and number of contacts

Existing exact results for the percolation probability and mean cluster siz e for compact percolation near a dry wall are extended to the mean cluster length and the mean number of contacts with the wall. The results are deriv ed from our previous work on vesicles near an attractive wall and involve e lliptic integrals as opposed to the simple rational forms found for the per colation probability and cluster size below p(c). The results for the clust er length satisfy previously conjectured differential equations. A closed e xpression is conjectured for the mean size above p(c) in terms of a hyperge ometric function.