Grassmann integral representation for spanning hyperforests

Sergio Caracciolo; Alan D. Sokal; Andrea Sportiello

doi:10.1088/1751-8113/40/46/001

Grassmann integral representation for spanning hyperforests

Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	13799-13835
Number of pages	37
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	46
DOIs	https://doi.org/10.1088/1751-8113/40/46/001
State	Published - Nov 16 2007

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

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Grassmann integral representation for spanning hyperforests

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