Abstract matrix-tree theorem and Bernardi polynomial
Combinatorics
2017-03-14 v1
Abstract
This paper is a continuation of arXiv:1612.03873. We prove a three-parameter family of identities (Theorem 1.1) involving a version of the Tutte polynomial for directed graphs introduced by Awan and Bernardi in arXiv:1610.01839. A particular case of this family (Corollary 1.6) is the higher-degree generalization of the matrix-tree theorem proved in arXiv:1612.03873, which thus receives a new proof, shorter (and less direct) than the original one. The theory has a parallel version for undirected graphs (Theorem 1.2).
Keywords
Cite
@article{arxiv.1703.04120,
title = {Abstract matrix-tree theorem and Bernardi polynomial},
author = {Yurii Burman},
journal= {arXiv preprint arXiv:1703.04120},
year = {2017}
}