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We study the generating function of rooted and unrooted hyperforests in ageneral complete hypergraph with n vertices by using a novel Grassmannrepresentation of their generating functions. We show that this new approachencodes the known results about the exponential generating functions for thedifferent number of vertices. We consider also some applications as countinghyperforests in the k-uniform complete hypergraph and the one complete inhyperedges of all dimensions. Some general feature of the asymptotic regimesfor large number of connected components is discussed.

Hyperforests on the Complete Hypergraph by Grassmann Integral Representation