A new matrix-tree theorem

By Gregor Masbaum, A. Vaintrob. 2001

49 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/231a61419fafee473a6d5c66219e9de0d2e196a2

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In Discrete Mathematics and Combinatorics

  1. Russell Lyons
  2. Eric Katz

In Geometry and Topology

  1. Caroline J. Klivans
  2. Jeremy L. Martin
  3. Art M. Duval

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