  We study the generating function of rooted and unrooted hyperforests in a
general complete hypergraph with n vertices by using a novel Grassmann
representation of their generating functions. We show that this new approach
encodes the known results about the exponential generating functions for the
different number of vertices. We consider also some applications as counting
hyperforests in the k-uniform complete hypergraph and the one complete in
hyperedges of all dimensions. Some general feature of the asymptotic regimes
for large number of connected components is discussed.
