Hyperforests on the Complete Hypergraph by Grassmann Integral Representation
Mathematical Physics
2008-11-26 v1 Statistical Mechanics
High Energy Physics - Lattice
Combinatorics
math.MP
Abstract
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.
Cite
@article{arxiv.0802.1506,
title = {Hyperforests on the Complete Hypergraph by Grassmann Integral Representation},
author = {Andrea Bedini and Sergio Caracciolo and Andrea Sportiello},
journal= {arXiv preprint arXiv:0802.1506},
year = {2008}
}
Comments
35 pages