Around matrix-tree theorem

Details Around matrix-tree theorem Around matrix-tree theorem

2005-12-07

arxiv.org/abs/math/0512164v2

Mathematics

Combinatorics

13 pages, no figures

Scientific paper

Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical theorem corresponds to the $A_n$-case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynomial, are of independent interest.

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