Around matrix-tree theorem [article]

Yurii Burman, Boris Shapiro
2006 arXiv   pre-print
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.
arXiv:math/0512164v2 fatcat:2u5ep3lrljfmvf4iz2z6bg62fm