Grassmann integral representation for spanning hyperforests

Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticlepeer-review


    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 languageEnglish (US)
    Pages (from-to)13799-13835
    Number of pages37
    JournalJournal of Physics A: Mathematical and Theoretical
    Issue number46
    StatePublished - 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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