A New Matrix-Tree Theorem

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The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have exactly three vertices) the spanning trees are generated by the Pfaffian of a suitably defined matrix. This result can be interpreted topologically as an expression for the lowest order term of the Alexander-Conway polynomial of an algebraically split link. We also prove some algebraic properties of our Pfaffian-tree polynomial.
minor changes, 29 pages, version accepted for publication in Int. Math. Res. Notices

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Combinatorics, Geometric Topology, Quantum Algebra, 05C50 (Primary); 15A15; 57M27 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/62204

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0109104
 http://arxiv.org/abs/math/0109104

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arXiv