Spanning forests and the vector bundle Laplacian

Preprint, Other literature type English OPEN
Kenyon, Richard;
(2011)
  • Publisher: The Institute of Mathematical Statistics
  • Journal: issn: 0091-1798
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1214/10-AOP596
  • Subject: resistor network | Mathematical Physics | quaternion | Mathematics - Probability | spanning tree | 82B20 | Discrete Laplacian
    acm: MathematicsofComputing_DISCRETEMATHEMATICS

The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial interpretation of their determ... View more
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