The multivariate signed Bollobas-Riordan polynomial
Combinatorics
2009-10-23 v2
Abstract
We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak [Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial Z and study its properties. We prove the invariance of Z under the recently defined partial duality of S. Chmutov [J. Combinatorial Theory, Ser. B, 99 (3): 617-638, 2009] and show that the duality transformation of the multivariate Tutte polynomial is a direct consequence of it.
Cite
@article{arxiv.0811.1584,
title = {The multivariate signed Bollobas-Riordan polynomial},
author = {Fabien Vignes-Tourneret},
journal= {arXiv preprint arXiv:0811.1584},
year = {2009}
}
Comments
17 pages, 2 figures. Published version: a section added about the quasi-tree expansion of the multivariate Bollobas-Riordan polynomial