Grassmann integral representation for spanning hyperforests

Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)13799-13835
    Number of pages37
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume40
    Issue number46
    DOIs
    StatePublished - Nov 16 2007

    Fingerprint

    Supersymmetry
    Integral Representation
    Algebra
    Matrix-tree Theorem
    Hypertree
    Grassmann Algebra
    vector spaces
    Hypergraph
    supersymmetry
    Generating Function
    apexes
    theorems
    expansion
    matrices
    Vertex of a graph
    Class

    ASJC Scopus subject areas

    • Mathematical Physics
    • Modeling and Simulation
    • Statistics and Probability
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics

    Cite this

    Grassmann integral representation for spanning hyperforests. / Caracciolo, Sergio; Sokal, Alan D.; Sportiello, Andrea.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 46, 16.11.2007, p. 13799-13835.

    Research output: Contribution to journalArticle

    Caracciolo, Sergio ; Sokal, Alan D. ; Sportiello, Andrea. / Grassmann integral representation for spanning hyperforests. In: Journal of Physics A: Mathematical and Theoretical. 2007 ; Vol. 40, No. 46. pp. 13799-13835.
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