SIMPLICIAL MATRIX-TREE THEOREMS

@inproceedings{Klivans2007SIMPLICIALMT,
  title={SIMPLICIAL MATRIX-TREE THEOREMS},
  author={Caroline J. Klivans and Jeremy L. Martin},
  year={2007}
}
We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes ∆, extending an idea due to G. Kalai. We prove a simplicial version of the Matrix-Tree Theorem that counts simplicial spanning trees, weighted by the squares of the orders of their top-dimensional integral homology groups, in terms of the Laplacian matrix of ∆. As in the graphic case, one can obtain a more finely weighted generating function for… CONTINUE READING
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