Generating functions for connected embeddings in a lattice. I. Strong embeddings

The method of partial generating functions developed to derive high field expansions for the Ising model enumerates unrestricted strong embeddings in a lattice. The method is modified to enumerate connected embeddings only. An explicit general receipt is given for the relation between unrestricted and restricted generating functions. For the body-centred cubic lattice the number of connected strong embeddings of clusters with up to 13 sites is derived.