Grassmann Integral Representation for Spanning Hyperforests

Understand

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests.

• Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees.
• All these results are generalizations of Kirchhoff's matrix-tree theorem.
• Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.