Hyperforests on the Complete Hypergraph by Grassmann Integral Representation
arXiv:0802.1506 · doi:10.1088/1751-8113/41/20/205003
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.
35 pages
References in corpus (5)
- The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
- Fermionic field theory for trees and forests
- Spanning forests and the q-state Potts model in the limit q \to 0
- Grassmann Integral Representation for Spanning Hyperforests
- Renormalization flow for unrooted forests on a triangular lattice