Knots and Graphs
نویسنده
چکیده
A classical matrix-tree theorem expresses the determinant of some matrix constructed from a graph (principal minor of the Laplacian) as a sum over all spanning trees of the graph. There are generalizations of this theorem to hypergraphs or simplicial complexes [MV, DKM]. Some version of this theorem provides a formula for the first non-zero coefficient of the Conway polynomial of a (virtual) link. In the case of graphs, the generating function of the spanning trees appears as a free term of the multivariable Tutte polynomial. The Tutte polynomial was generalized to simplicial complexes in [KR]. The aim of this project is to relate the free terms of the Krushkal-Renardy polynomial with the simplicial matrix-tree theorem.
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