Hyperforests on the complete hypergraph by Grassmann integral representation.

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 also consider some applications, such as counting hyperforests in the k-uniform complete hypergraph and the one complete in hyperedges of all dimensions. Some general features of the asymptotic regimes for a large number of connected components are discussed. [ABSTRACT FROM AUTHOR]