Principal minors Pfaffian half-tree theorem

Abstract : A half-tree is an edge configuration whose superimposition with a perfect matching is a tree. In this paper, we prove a half-tree theorem for the Pfaffian principal minors of a skew-symmetric matrix whose column sum is zero; introducing an explicit algorithm, we fully characterize half-trees involved. This question naturally arose in the context of statistical mechanics where we aimed at relating perfect matchings and trees on the same graph. As a consequence of the Pfaffian half-tree theorem, we obtain a refined version of the matrix-tree theorem in the case of skew-symmetric matrices, as well as a line-bundle version of this result.
Type de document :
Pré-publication, Document de travail
34 pages, 10 figures. 2012
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Contributeur : Béatrice De Tilière <>
Soumis le : mardi 24 juillet 2012 - 14:16:59
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

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  • HAL Id : hal-00720394, version 1
  • ARXIV : 1207.2759



Béatrice De Tilière. Principal minors Pfaffian half-tree theorem. 34 pages, 10 figures. 2012. 〈hal-00720394〉



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