Exact generating function for fully directed compact lattice animals.

The fully directed compact lattice-animal model on the square lattice is solved exactly. An explicit expression is obtained for the cluster-number generating function which has a complicated complexplane singularity pattern including a natural boundary of essential singularities. However, the cluster numbers are controlled by a simple pole singularity and grow proportionally to X, where TV is the number of sites, and X = 2.66.